Channel encoding method and apparatus in wireless communications

ABSTRACT

This application provides a channel encoding method and apparatus in wireless communications. The method includes: performing CRC encoding on A to-be-encoded information bits, to obtain a first bit sequence, where the first bit sequence includes L CRC bits and A information bits; performing an interleaving operation on the first bit sequence, to obtain a second bit sequence, where a first interleaving sequence used for the interleaving operation is obtained based on a system-supported maximum-length interleaving sequence with the length of Kmax+L, and Kmax is a maximum information bit quantity corresponding to the maximum-length interleaving sequence and a preset rule, and a length of the first interleaving sequence is equal to A+L. Therefore, during distributed CRC encoding, when an information bit quantity is less than the maximum information bit quantity, an interleaving sequence required for completing an interleaving process is obtained based on the system-supported maximum-length interleaving sequence.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/CN2018/086329, filed on May 10, 2018, which claims priority toChinese Patent Application No. 201710667569.7, filed on Aug. 7, 2017.The disclosures of the aforementioned applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

This application relates to the field of communications technologies,and in particular, to an encoding method and apparatus.

BACKGROUND

Channel encoding is usually used in a communications system, to improvedata transmission reliability and ensure communication quality. A polar(polar) code is the first channel encoding method that can be strictlyproved to “achieve” a channel capacity. The polar code is a type oflinear block code, a generator matrix of the polar code is G_(N), anencoding process of the polar code is x₁ ^(N)=u₁ ^(N)G_(N), and u₁^(N)=(u₁, u₂, . . . , u_(N)) is a binary row vector with a length N(namely, a code length). G_(N)=B_(N)F₂ ^(⊗(log) ² ^((N))). Herein,

${F_{2} = \begin{bmatrix}1 & 0 \\1 & 1\end{bmatrix}},$

B_(N) is an N×N transposed matrix, for example, a bit-reversal-ordertransposed matrix, F₂ ^(⊗(log) ² ^((N))) is defined as a Kronecker(Kronecker) product of log₂ N matrices F₂, x₁ ^(N) is encoded bits (alsoreferred to as a code word), and the encoded bits are obtained after u₁^(N) is multiplied by the generator matrix G_(N). A multiplicationprocess is the encoding process. In the encoding process of the polarcode, some bits in u₁ ^(N) are used to carry information and arereferred to as information bits, and an index set of the informationbits is denoted as A. The other bits in u₁ ^(N) are set to fixed valuesthat are agreed on by a transmit end and a receive end in advance, andare referred to as frozen bits, and an index set of the frozen bits isrepresented by a complementary set A^(c) of A. The frozen bits areusually set to 0. A sequence of the frozen bits may be set to any valuesif the transmit end and the receive end reach an agreement in advance.To improve performance of the polar code, an outer code with a checkcapability may be concatenated with the polar code. CA-polar code is apolar code concatenated with a cyclic redundancy check (CRC) code.

An encoding process of the CA-polar code is as follows: CRC encoding isperformed on information bits of to-be-encoded information, to obtain abit sequence after the CRC encoding, where the bit sequence obtainedafter the CRC encoding includes information bits and CRC bits; then,polar encoding is performed on the bit sequence obtained after the CRCencoding. A CA-SCL (CRC-Aided Successive Cancellation List) decodingalgorithm is used for decoding the CA-polar code. After SCL decodingends, CRC check is performed on L candidate paths that are output afterthe SCL decoding, and a candidate path whose CRC check succeeds is usedas a decoding output result. If there is no candidate path whose CRCcheck succeeds, it is determined that the decoding fails. Therefore, forthe CA-polar code, CRC check can be performed only after channeldecoding ends, and time occupied for a failed decoding process is thesame as time occupied for a successful decoding process. In a scenarioof downlink blind detection on a control channel in a wirelesscommunications system, dozens of decoding attempts usually need to bemade, but a maximum of one decoding attempt can succeed. If a decodingattempt that results in a decoding failure can be stopped in advance(early termination), a decoding delay and average energy consumption ofthe entire blind detection can be effectively reduced. Distributed CRCencoding is put forward as a CRC encoding manner with an “earlytermination” capability. During the distributed CRC encoding, aninterleaving operation is introduced after conventional CRC encodingends; to be specific, CRC bits obtained after CRC encoding aredistributed among information bits. In an SCL decoding process of adecoder, at a moment before decoding ends, when none of candidate pathscan meet check of some CRC bits that have been decoded, the decoding canend in advance.

The interleaving operation is performed by using a pre-storedinterleaving sequence. Because a CRC encoding process is related to aninformation bit quantity, a length of the interleaving sequence is thesame as the information bit quantity. If a system needs to support anexcessively large quantity of information bits, the system needs tostore a large quantity of interleaving sequences. Consequently, systemstorage overheads are relatively high.

SUMMARY

This application provides an encoding method and apparatus, so thatduring distributed CRC encoding, when an information bit quantity isless than a maximum information bit quantity, an interleaving sequencerequired for completing an interleaving process is obtained based on asystem-supported maximum-length interleaving sequence.

According to a first aspect, this application provides an encodingmethod, including: performing cyclic redundancy check (CRC) encoding onA to-be-encoded information bits, to obtain a first bit sequence, wherethe first bit sequence includes L CRC bits and A information bits, and Land A are positive integers; performing an interleaving operation on thefirst bit sequence, to obtain a second bit sequence, where a firstinterleaving sequence used for the interleaving operation is obtainedbased on a system-supported maximum-length interleaving sequence and apreset rule, and a length of the first interleaving sequence is equal toA+L; or a second interleaving sequence used for the interleavingoperation is the maximum-length interleaving sequence, a length of thesecond interleaving sequence is equal to K_(max)+L, and K_(max) is amaximum information bit quantity corresponding to the maximum-lengthinterleaving sequence; and performing polar encoding on the second bitsequence.

According to the encoding method provided in the first aspect, atransmit end performs CRC encoding on the A to-be-encoded informationbits, to obtain the first bit sequence, and then performs theinterleaving operation on the first bit sequence, to obtain the secondbit sequence. The first interleaving sequence used for the interleavingoperation is obtained based on the maximum-length interleaving sequenceand the preset rule, and the length of the first interleaving sequencecorresponds to the quantity of to-be-encoded information bits.Alternatively, the second interleaving sequence used for theinterleaving operation is directly the maximum-length interleavingsequence. Finally, the transmit end performs polar encoding on thesecond bit sequence. Therefore, during distributed CRC encoding, when aninformation bit quantity is less than the maximum information bitquantity, an interleaving sequence required for completing aninterleaving process is obtained based on the system-supportedmaximum-length interleaving sequence.

In a possible design, the preset rule is: the first interleavingsequence is constituted by sequentially extracting all indexes greaterthan or equal to K_(max)−A from the maximum-length interleaving sequenceand subtracting K_(max)−A from each of all the extracted indexes; andthe performing an interleaving operation on the first bit sequenceincludes: performing the interleaving operation on the first bitsequence by using the first interleaving sequence, to obtain the secondbit sequence.

According to the encoding method provided in this implementation, whenthe interleaving operation is performed by using the first interleavingsequence, parallel processing may be used during an operation ofobtaining the first interleaving sequence based on the maximum-lengthinterleaving sequence and the preset rule. After the first interleavingsequence is obtained, the second bit sequence may be directly obtainedby performing the interleaving operation on the first interleavingsequence, so that a delay can be reduced, thereby reducing an encodingdelay.

In a possible design, the preset rule is: the first interleavingsequence is constituted by sequentially extracting all indexes less thanA or greater than or equal to K_(max) from the maximum-lengthinterleaving sequence and subtracting K_(max)−A from indexes greaterthan or equal to K_(max) in the extracted indexes; and the performing aninterleaving operation on the first bit sequence includes: arranging theA information bits in the first bit sequence in descending order ofinformation bit indexes, to obtain a third bit sequence; and performingthe interleaving operation on the third bit sequence by using the firstinterleaving sequence, to obtain the second bit sequence.

According to the encoding method provided in this implementation, whenthe interleaving operation is performed by using the first interleavingsequence, parallel processing may be used during an operation ofobtaining the first interleaving sequence based on the maximum-lengthinterleaving sequence and the preset rule. After the first interleavingsequence is obtained, the second bit sequence may be directly obtainedby performing the interleaving operation on the first interleavingsequence, so that a delay can be reduced, thereby reducing an encodingdelay.

In a possible design, when the second interleaving sequence used for theinterleaving operation is the maximum-length interleaving sequence, theperforming an interleaving operation on the first bit sequence includes:extending the first bit sequence to a fourth bit sequence includingK_(max)+L bits, where values of first K_(max)−A bits in the fourth bitsequence are set to NULL, and remaining bits sequentially correspond tothe bits in the first bit sequence from a (K_(max)−A+1)^(th) bit;performing the interleaving operation on the fourth bit sequence byusing the maximum-length interleaving sequence, to obtain a fifth bitsequence; and removing, from the fifth bit sequence, the bits whosevalues are NULL, to obtain the second bit sequence.

In a possible design, the maximum-length interleaving sequence is anysequence in Table 1 in this specification.

In a possible design, the maximum-length interleaving sequence is anysequence in Table 2 in this specification.

According to a second aspect, this application provides an encodingapparatus, including: a first encoding module, configured to performcyclic redundancy check (CRC) encoding on A to-be-encoded informationbits, to obtain a first bit sequence, where the first bit sequenceincludes L CRC bits and A information bits, and L and A are positiveintegers; an interleaving module, configured to perform an interleavingoperation on the first bit sequence, to obtain a second bit sequence,where a first interleaving sequence used for the interleaving operationis obtained based on a system-supported maximum-length interleavingsequence and a preset rule, and a length of the first interleavingsequence is equal to A+L; or a second interleaving sequence used for theinterleaving operation is the maximum-length interleaving sequence, alength of the second interleaving sequence is equal to K_(max)+L, andK_(max) is a maximum information bit quantity corresponding to themaximum-length interleaving sequence; and a second encoding module,configured to perform polar encoding on the second bit sequence.

In a possible design, the preset rule is: the first interleavingsequence is sequentially constituted by extracting all indexes greaterthan or equal to K_(max)−A from the maximum-length interleaving sequenceand subtracting K_(max)−A from each of all the extracted indexes; andthe interleaving module is configured to perform the interleavingoperation on the first bit sequence by using the first interleavingsequence, to obtain the second bit sequence.

In a possible design, the preset rule is: the first interleavingsequence is constituted by sequentially extracting all indexes less thanA or greater than or equal to K_(max) from the maximum-lengthinterleaving sequence and subtracting K_(max)−A from indexes greaterthan or equal to K_(max) in the extracted indexes; and the interleavingmodule is configured to: arrange the A information bits in the first bitsequence in descending order of information bit indexes, to obtain athird bit sequence; and perform the interleaving operation on the thirdbit sequence by using the first interleaving sequence, to obtain thesecond bit sequence.

In a possible design, when the second interleaving sequence used for theinterleaving operation is the maximum-length interleaving sequence, theinterleaving module is configured to: extend the first bit sequence to afourth bit sequence including K_(max)+L bits, where values of firstK_(max)−A bits in the fourth bit sequence are set to NULL, and remainingbits sequentially correspond to the bits in the first bit sequence froma (K_(max)−A+1)^(th) bit; perform the interleaving operation on thefourth bit sequence by using the maximum-length interleaving sequence,to obtain a fifth bit sequence; and obtain the second bit sequence byremoving the bits whose values are NULL from the fifth bit sequence.

In a possible design, the maximum-length interleaving sequence is anysequence in Table 1 in this specification.

In a possible design, the maximum-length interleaving sequence is anysequence in Table 2 in this specification.

For beneficial effects of the encoding apparatus provided in the secondaspect and the possible designs of the second aspect, refer to thebeneficial effects brought by the first aspect and the possibleimplementations of the first aspect. Details are not described hereinagain.

According to a third aspect, this application provides an encodingapparatus, including a memory and a processor, where

the memory is configured to store a program instruction; and

the processor is configured to invoke the program instruction in thememory, to perform the encoding method according to the first aspect andany possible design of the first aspect.

According to a fourth aspect, this application provides a readablestorage medium, including a readable storage medium and a computerprogram, where the computer program is used to implement the methodaccording to the first aspect and any possible design of the firstaspect.

According to a fifth aspect, this application provides a programproduct, where the program product includes a computer program, thecomputer program is stored in a readable storage medium, at least oneprocessor of an encoding apparatus may read the computer program fromthe readable storage medium, and the at least one processor executes thecomputer program, so that the encoding apparatus implements the methodaccording to the first aspect and any possible design of the firstaspect.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a system architecture including atransmit end and a receive end according to this application;

FIG. 2 is a schematic flowchart of a communications system;

FIG. 3 is a flowchart of an embodiment of an encoding method accordingto this application;

FIG. 4 is a schematic flowchart of an encoding method according to thisapplication;

FIG. 5 is a schematic flowchart of an encoding method according to thisapplication;

FIG. 6 is a schematic flowchart of an encoding method according to thisapplication;

FIG. 7 is a schematic structural diagram of an embodiment of an encodingapparatus according to this application;

FIG. 8 is a schematic diagram of an encoding entity apparatus accordingto this application; and

FIG. 9 is a schematic diagram of an encoding entity apparatus accordingto this application.

DESCRIPTION OF EMBODIMENTS

The embodiments of this application may be applied to a wirelesscommunications system. It should be noted that the wirelesscommunications system mentioned in the embodiments of this applicationincludes but is not limited to a Narrowband Internet of Things (NB-IoT)system, the Global System for Mobile Communications (GSM), an EnhancedData rates for GSM Evolution (EDGE) system, a Wideband Code DivisionMultiple Access (WCDMA) system, a Code Division Multiple Access 2000(CDMA2000) system, a Time Division-Synchronous Code Division MultipleAccess (TD-SCDMA) system, a Long Term Evolution (LTE) system, and threeapplication scenarios in a next-generation 5G mobile communicationssystem: the Enhanced Mobile Broadband eMBB), URLLC, and massive machinetype communications (mMTC).

Communications apparatuses related in this application mainly include anetwork device and a terminal device. In this application, if a transmitend is the network device, a receive end is the terminal device. In thisapplication, if a transmit end is the terminal device, a receive end isthe network device.

In the embodiments of this application, the terminal device (terminaldevice) includes but is not limited to a mobile station (MS), a mobileterminal, a mobile telephone, a handset, a portable equipment, and thelike. The terminal device may communicate with one or more core networksby using a radio access network (RAN). For example, the terminal devicemay be a mobile phone (or referred to as a “cellular” phone), or acomputer with a wireless communication function. Alternatively, theterminal device may be a portable, pocket-sized, handheld, computerbuilt-in, or in-vehicle mobile apparatus or device.

The embodiments are described in this application with reference to thenetwork device. The network device may be a device configured tocommunicate with the terminal device. For example, the network devicemay be a base transceiver station (BTS) in the GSM system or CDMA, maybe a NodeB (NB) in the WCDMA system, or may be an evolved NodeB (eNB oreNodeB) in the LTE system. Alternatively, the network device may be arelay station, an access point, an in-vehicle device, a wearable device,a network-side device in a future 5G network, a network device in afuture evolved public land mobile network (Public Land Mobile Network,PLMN), or the like. Alternatively, the network device may be a terminaldevice responsible for a network device function during D2Dcommunication.

A communications system in this application may include a transmit endand a receive end. FIG. 1 is a schematic diagram of a systemarchitecture including a transmit end and a receive end according tothis application. As shown in FIG. 1, the transmit end is an encoderside, and may be configured to perform encoding and output encodedinformation. The encoded information is transmitted to a decoder side ona channel. The receive end is the decoder side, and may be configuredto: receive the encoded information sent by the transmit end, and decodethe encoded information.

FIG. 2 is a schematic flowchart of a communications system. As shown inFIG. 2, at a transmit end, a signal source sequentially undergoes signalsource encoding, channel encoding, interleaving, rate matching, anddigital modulation. At a receive end, the signal source sequentiallyundergoes digital demodulation, rate de-matching, channel decoding, andsignal source decoding, and is output to a signal sink. A polar code ora CA-polar code may be used for the channel encoding/decoding. Anencoding method provided in this application may be used for the channelencoding.

This application provides an encoding method and apparatus, so thatduring distributed CRC encoding, when an information bit quantity isless than a maximum information bit quantity, an interleaving sequencerequired for completing an interleaving process is obtained based on asystem-supported maximum-length interleaving sequence, and betterperformance can be ensured. For example, an encoding delay is reduced,and a false alarm probability is decreased. An information bit quantitycorresponding to the system-supported maximum-length interleavingsequence is the maximum information bit quantity. The encoding methodand apparatus that are provided in this application are described belowin detail with reference to the accompanying drawings.

It should be noted that, to complete an interleaving function, there aretwo numbering manners for an interleaving sequence: information bits arenumbered in natural order, or information bits are numbered in reverseorder (briefly referred to as natural-order numbering and reverse-ordernumbering below). The natural-order numbering means that a ranking of anindex of a corresponding information bit in an interleaving sequence isthe same as a ranking of the index of the information bit; to bespecific, an index 0 corresponds to a 0th information bit, an index 1corresponds to a first information bit, and so on. The reverse-ordernumbering means that a ranking of an index of a correspondinginformation bit in an interleaving sequence is reverse to a ranking ofthe index of the information bit; to be specific, an index 0 correspondsto the last information bit, an index 1 corresponds to the penultimateinformation bit, and so on.

In addition, a minimum index of the interleaving sequence related in theembodiments of this application is 0. If a minimum index of an actuallyused interleaving sequence is 1, the method in this application may besimply adjusted. In all examples in this application, an interleavingsequence starts with an index 0. During actual application, if aninterleaving sequence starts with an index 1, each corresponding indexis increased by 1.

FIG. 3 is a flowchart of an embodiment of an encoding method accordingto this application. As shown in FIG. 3, this embodiment is performed bya transmit end (an encoder). The method in this embodiment may includethe following steps.

S101. The transmit end performs CRC encoding on A to-be-encodedinformation bits, to obtain a first bit sequence, where the first bitsequence includes L CRC bits and A information bits, and L and A arepositive integers.

Specifically, after receiving the A to-be-encoded information bits, thetransmit end adds the L CRC bits, to obtain the first bit sequence.

S102. The transmit end performs an interleaving operation on the firstbit sequence, to obtain a second bit sequence.

Two types of interleaving sequences are used for the interleavingoperation: a first interleaving sequence and a second interleavingsequence. Different interleaving sequences correspond to differentinterleaving operations. The first interleaving sequence is obtainedbased on a system-supported maximum-length interleaving sequence and apreset rule, and a length of the first interleaving sequence is equal toA+L. The second interleaving sequence is the maximum-length interleavingsequence, a length of the second interleaving sequence is equal toK_(max)+L, and K_(max) is a maximum information bit quantitycorresponding to the maximum-length interleaving sequence. Thesystem-supported maximum-length interleaving sequence is brieflyreferred to as the maximum-length interleaving sequence below.

The system-supported maximum-length interleaving sequence may bepre-stored, or may be obtained through online calculation.

The first interleaving sequence may be obtained in two manners thatrespectively correspond to two types of preset rules.

In Manner 1, the preset rule is: the first interleaving sequence isconstituted by sequentially extracting all indexes greater than or equalto K_(max)−A from the maximum-length interleaving sequence andsubtracting K_(max)−A from each of all the extracted indexes. Forexample, the maximum-length interleaving sequence is {2, 3, 5, 9, 10,12, 4, 6, 11, 13, 0, 7, 14, 1, 8, 15}, the maximum information bitquantity K_(max) corresponding to the maximum-length interleavingsequence is equal to 12, L=4, A=10, and K_(max)−A=2. All indexes {2, 3,5, 9, 10, 12, 4, 6, 11, 13, 7, 14, 8, 15} greater than or equal to 2 arefirst sequentially extracted from the maximum-length interleavingsequence, and 2 is subtracted from each of all the extracted indexes, toconstitute the first interleaving sequence {0, 1, 3, 7, 8, 10, 2, 4, 9,11, 5, 12, 6, 13}.

Correspondingly, the performing, by the transmit end, an interleavingoperation on the first bit sequence may be specifically: performing, bythe transmit end, the interleaving operation on the first bit sequenceby using the first interleaving sequence, to obtain the second bitsequence.

In Manner 1, natural-order numbering is used for the maximum-lengthinterleaving sequence.

In Manner 2, the preset rule is: the first interleaving sequence isconstituted by sequentially extracting all indexes less than A orgreater than or equal to K_(max) from the maximum-length interleavingsequence and subtracting K_(max)−A from indexes greater than or equal toK_(max) in the extracted indexes. For example, the maximum-lengthinterleaving sequence is {1, 2, 6, 8, 9, 12, 0, 5, 7, 13, 4, 11, 14, 3,10, 15}, the maximum information bit quantity K_(max) corresponding tothe maximum-length interleaving sequence is equal to 12, L=4, A=10, andK_(max)−A=2. All indexes {1, 2, 6, 8, 9, 12, 0, 5, 7, 13, 4, 14, 3, 15}less than 10 or greater than or equal to 12 are first sequentiallyextracted from the maximum-length interleaving sequence, and 2 issubtracted from indexes greater than or equal to 12 in the extractedindexes, to constitute the first interleaving sequence {1, 2, 6, 8, 9,10, 0, 5, 7, 11, 4, 12, 3, 13}.

Correspondingly, the performing, by the transmit end, an interleavingoperation on the first bit sequence may be specifically: arranging, bythe transmit end, the A information bits in the first bit sequence indescending order of information bit indexes, to obtain a third bitsequence. Arrangement in descending order is also referred to asarrangement in reverse order. For example, the first bit sequence is {0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, {0, 1, 2, 3, 4, 5, 6, 7,8, 9, 10} are the information bits, and {11, 12, 13, 14} are the CRCbits. {10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0} is obtained after theinformation bits are arranged in reverse order, and the obtained thirdbit sequence is {10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 12, 13, 14}.Then, the transmit end performs the interleaving operation on the thirdbit sequence by using the first interleaving sequence, to obtain thesecond bit sequence.

In Manner 2, reverse-order numbering is used for the maximum-lengthinterleaving sequence.

The maximum-length interleaving sequence may be directly used as thesecond interleaving sequence. Correspondingly, the performing, by thetransmit end, an interleaving operation on the first bit sequence may bespecifically:

extending, by the transmit end, the first bit sequence to a fourth bitsequence including K_(max)+L bits, where values of first K_(max)−A bitsin the fourth bit sequence are set to NULL, and remaining bitssequentially correspond to the bits in the first bit sequence from a(K_(max)−A+1)^(th) bit.

For example, K_(max)=12, L=4, A=10, and K_(max)−A=2. The transmit endextends the first bit sequence (including four CRC bits and 10information bits) to the fourth bit sequence including 12+4=16 bits.Values of first two bits in the fourth bit sequence are set to NULL, andremaining bits sequentially correspond to the bits in the first bitsequence from a third bit.

The transmit end performs the interleaving operation on the fourth bitsequence by using the maximum-length interleaving sequence, to obtain afifth bit sequence.

The transmit end obtain the second bit sequence by removing the bitswhose values are NULL from the fifth bit sequence.

When the interleaving operation is performed by using the secondinterleaving sequence, the first bit sequence needs to be extendedbefore the interleaving, and after the interleaving, the bits whosevalues are NULL need to be removed from the interleaved bit sequence.Therefore, an interleaving operation delay is relatively long. Incomparison with performing the interleaving operation by using thesecond interleaving sequence, when the interleaving operation isperformed by using the first interleaving sequence, parallel processingmay be used during an operation of obtaining the first interleavingsequence based on the maximum-length interleaving sequence and thepreset rule, and after the first interleaving sequence is obtained, thesecond bit sequence may be directly obtained by performing theinterleaving operation by using the first interleaving sequence, so thata delay can be reduced, thereby reducing an encoding delay.

In this manner, natural-order numbering is used for the maximum-lengthinterleaving sequence.

S103. The transmit end performs polar encoding on the second bitsequence.

The transmit end may perform polar encoding on the second bit sequenceby using an existing polar encoding method. Details are not describedherein.

According to the encoding method provided in this embodiment, thetransmit end performs CRC encoding on the A to-be-encoded informationbits, to obtain the first bit sequence, and then performs theinterleaving operation on the first bit sequence, to obtain the secondbit sequence. The first interleaving sequence used for the interleavingoperation is obtained based on the maximum-length interleaving sequenceand the preset rule, and the length of the first interleaving sequencecorresponds to the quantity of to-be-encoded information bits.Alternatively, the second interleaving sequence used for theinterleaving operation is directly the maximum-length interleavingsequence. Finally, the transmit end performs polar encoding on thesecond bit sequence. Therefore, during distributed CRC encoding, when aninformation bit quantity is less than the maximum information bitquantity, an interleaving sequence required for completing aninterleaving process is obtained based on the system-supportedmaximum-length interleaving sequence.

The technical solutions in the method embodiment shown in FIG. 3 aredescribed in detail below by using several specific embodiments.

FIG. 4 is a schematic flowchart of an encoding method according to thisapplication. In this embodiment, for example, an interleaving sequenceused for an interleaving operation is the first interleaving sequenceobtained based on the preset rule in Manner 1, a maximum-lengthinterleaving sequence used for distributed CRC encoding is a sequence η1for which natural-order numbering is used, a maximum information bitlength corresponding to the interleaving sequence π1 is K_(max), a CRCpolynomial is g, and a CRC bit quantity is L. In other words, a CRClength is L. It is assumed that A to-be-encoded information bits are{a₀, a₁, . . . , a_(A−1)}, and the information bit quantity A≤K_(max).This embodiment is performed by a transmit end (an encoder). As shown inFIG. 4, the method in this embodiment includes the following steps.

S201. Perform CRC encoding on A to-be-encoded information bits, toobtain a first bit sequence {b₀, b₁, . . . , b_(A+L-1)}.

{b₀, b₁, . . . , b_(A−1)} are A information bits, and {b_(A), b_(A+1), .. . , b_(A+L-1)} are L CRC bits.

S202. the first interleaving sequence π1′ is constituted by sequentiallyextracting all indexes less than A or greater than or equal to K_(max)from the maximum-length interleaving sequence and subtracting K_(max)−Afrom indexes greater than or equal to K_(max) in the extracted indexes

For example, as shown in FIG. 4, if the maximum-length interleavingsequence π1 is {2, 3, 5, 9, 10, 12, 4, 6, 11, 13, 0, 7, 14, 1, 8, 15},L=4, and A=10, a maximum information bit quantity K_(max) correspondingto the maximum-length interleaving sequence is equal to 12, andK_(max)−A=2. All indexes greater than or equal to 2 are firstsequentially extracted from π1, and an extracted part is {2, 3, 5, 9,10, 12, 4, 6, 11, 13, 7, 14, 8, 15}. Then, 2 is subtracted from each ofall the extracted indexes, to constitute the first interleaving sequenceπ1′ {0, 1, 3, 7, 8, 10, 2, 4, 9, 11, 5, 12, 6, 13}.

S203. Perform an interleaving operation on the first bit sequence {b₀,b₁, . . . , b_(A+L-1)} by using the first interleaving sequence π1′, toobtain a second bit sequence {c₀, c₁, . . . , c_(A+L-1)}.

Specifically, the first bit sequence shown in FIG. 4 is {b₀, b₁, . . . ,b₁₃}. After the interleaving operation is performed on the first bitsequence {b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, b₉, b₁₀, b₁₁, b₁₂, b₁₃} byusing the first interleaving sequence π1′ {0, 1, 3, 7, 8, 10, 2, 4, 9,11, 5, 12, 6, 13}, the second bit sequence is obtained.

S204. Perform polar encoding on the second bit sequence.

In this embodiment, as shown in the following Table 1, for aninterleaving sequence in Table 1, different CRC polynomials andcorresponding interleaving sequences for which natural-order numberingis used are provided for different CRC lengths L and different maximuminformation bit quantities K_(max).

TABLE 1 CRC Interleaving sequence for which natural-order numbering isK_(max) L polynomial used 200 19 0xA2B79 0, 1, 2, 5, 6, 7, 10, 11, 13,14, 18, 19, 20, 22, 23, 24, 26, 31, 33, 35, 37, 39, 42, 44, 45, 47, 51,52, 55, 56, 57, 58, 60, 61, 62, 64, 67, 69, 70, 72, 73, 76, 85, 86, 89,90, 93, 94, 100, 103, 104, 105, 107, 109, 110, 112, 113, 125, 127, 128,129, 130, 131, 133, 134, 137, 140, 144, 145, 148, 149, 152, 159, 161,162, 163, 166, 169, 173, 175, 178, 182, 183, 186, 187, 189, 195, 196,197, 200, 3, 4, 8, 9, 12, 15, 16, 21, 25, 28, 41, 46, 49, 53, 54, 59,63, 66, 71, 74, 75, 78, 87, 88, 91, 92, 95, 96, 102, 106, 111, 114, 115,132, 135, 136, 139, 142, 146, 147, 150, 151, 154, 164, 165, 168, 171,177, 180, 184, 185, 188, 191, 198, 199, 202, 17, 27, 29, 34, 36, 38, 40,48, 50, 65, 79, 97, 108, 116, 143, 155, 172, 176, 181, 190, 192, 203,32, 43, 68, 77, 80, 98, 99, 101, 118, 121, 122, 126, 156, 160, 170, 179,194, 209, 81, 119, 123, 138, 153, 157, 210, 82, 117, 120, 124, 141, 158,167, 174, 193, 211, 30, 83, 212, 84, 201, 204, 205, 206, 207, 208, 213,214, 215, 216, 217, 218 200 19 0xA2B79 197, 196, 195, 189, 187, 186,183, 182, 178, 175, 173, 169, 166, 163, 162, 161, 159, 152, 149, 148,145, 144, 140, 137, 134, 133, 131, 130, 129, 128, 127, 125, 113, 112,110, 109, 107, 105, 104, 103, 100, 94, 93, 90, 89, 86, 85, 76, 73, 72,70, 69, 67, 64, 62, 61, 60, 58, 57, 56, 55, 52, 51, 47, 45, 44, 42, 39,37, 35, 33, 31, 26, 24, 23, 22, 20, 19, 18, 14, 13, 11, 10, 7, 6, 5, 2,1, 0, 200, 199, 198, 191, 188, 185, 184, 180, 177, 171, 168, 165, 164,154, 151, 150, 147, 146, 142, 139, 136, 135, 132, 115, 114, 111, 106,102, 96, 95, 92, 91, 88, 87, 78, 75, 74, 71, 66, 63, 59, 54, 53, 49, 46,41, 28, 25, 21, 16, 15, 12, 9, 8, 4, 3, 202, 192, 190, 181, 176, 172,155, 143, 116, 108, 97, 79, 65, 50, 48, 40, 38, 36, 34, 29, 27, 17, 203,194, 179, 170, 160, 156, 126, 122, 121, 118, 101, 99, 98, 80, 77, 68,43, 32, 209, 157, 153, 138, 123, 119, 81, 210, 193, 174, 167, 158, 141,124, 120, 117, 82, 211, 83, 30, 212, 84, 201, 204, 205, 206, 207, 208,213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2, 3, 4, 7, 8, 9, 12,13, 15, 16, 20, 21, 22, 24, 25, 26, 28, 33, 35, 37, 39, 41, 44, 46, 47,49, 53, 54, 57, 58, 59, 60, 62, 63, 64, 66, 69, 71, 72, 74, 75, 78, 87,88, 91, 92, 95, 96, 102, 105, 106, 107, 109, 111, 112, 114, 115, 127,129, 130, 131, 132, 133, 135, 136, 139, 142, 146, 147, 150, 151, 154,161, 163, 164, 165, 168, 171, 175, 177, 180, 184, 185, 188, 189, 191,197, 198, 199, 202, 6, 11, 17, 18, 19, 27, 29, 31, 34, 36, 38, 40, 48,50, 51, 52, 56, 65, 79, 85, 86, 90, 94, 97, 100, 104, 108, 116, 125,143, 144, 145, 149, 155, 159, 172, 173, 176, 181, 182, 183, 187, 190,192, 195, 196, 203, 23, 32, 43, 55, 61, 68, 76, 81, 89, 93, 98, 99, 101,103, 110, 117, 118, 126, 134, 137, 140, 141, 148, 152, 157, 160, 169,170, 179, 186, 194, 205, 5, 14, 30, 67, 77, 82, 119, 128, 138, 153, 158,162, 174, 193, 206, 10, 70, 80, 121, 122, 156, 209, 42, 120, 123, 124,167, 178, 211, 45, 83, 166, 212, 73, 84, 113, 200, 201, 204, 207, 208,210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197, 191,189, 188, 185, 184, 180, 177, 175, 171, 168, 165, 164, 163, 161, 154,151, 150, 147, 146, 142, 139, 136, 135, 133, 132, 131, 130, 129, 127,115, 114, 112, 111, 109, 107, 106, 105, 102, 96, 95, 92, 91, 88, 87, 78,75, 74, 72, 71, 69, 66, 64, 63, 62, 60, 59, 58, 57, 54, 53, 49, 47, 46,44, 41, 39, 37, 35, 33, 28, 26, 25, 24, 22, 21, 20, 16, 15, 13, 12, 9,8, 7, 4, 3, 2, 1, 0, 202, 196, 195, 192, 190, 187, 183, 182, 181, 176,173, 172, 159, 155, 149, 145, 144, 143, 125, 116, 108, 104, 100, 97, 94,90, 86, 85, 79, 65, 56, 52, 51, 50, 48, 40, 38, 36, 34, 31, 29, 27, 19,18, 17, 11, 6, 203, 194, 186, 179, 170, 169, 160, 157, 152, 148, 141,140, 137, 134, 126, 118, 117, 110, 103, 101, 99, 98, 93, 89, 81, 76, 68,61, 55, 43, 32, 23, 205, 193, 174, 162, 158, 153, 138, 128, 119, 82, 77,67, 30, 14, 5, 206, 156, 122, 121, 80, 70, 10, 209, 178, 167, 124, 123,120, 42, 211, 166, 83, 45, 212, 73, 84, 113, 200, 201, 204, 207, 208,210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 3, 4, 6, 7, 8, 9, 11,16, 17, 18, 19, 20, 21, 24, 25, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39,40, 44, 48, 50, 51, 52, 54, 56, 57, 59, 62, 63, 65, 69, 75, 79, 85, 86,88, 90, 92, 94, 96, 97, 100, 104, 105, 106, 108, 109, 115, 116, 125,127, 129, 132, 136, 143, 144, 145, 147, 149, 151, 155, 159, 161, 163,164, 165, 172, 173, 175, 176, 181, 182, 183, 185, 187, 190, 192, 195,196, 197, 198, 199, 203, 0, 1, 2, 12, 13, 14, 23, 28, 30, 32, 41, 42,47, 49, 53, 61, 66, 67, 72, 73, 80, 87, 91, 95, 98, 101, 103, 112, 113,117, 126, 131, 134, 140, 146, 150, 156, 160, 169, 174, 177, 178, 184,188, 189, 191, 193, 204, 15, 43, 55, 58, 60, 68, 74, 76, 81, 89, 93, 99,102, 110, 114, 118, 133, 135, 137, 141, 148, 152, 157, 170, 179, 186,194, 205, 5, 22, 77, 82, 107, 111, 119, 128, 138, 142, 153, 158, 162,171, 180, 206, 10, 26, 45, 64, 70, 78, 84, 120, 121, 139, 167, 208, 71,122, 123, 130, 166, 210, 46, 83, 213, 124, 154, 168, 200, 201, 202, 207,209, 211, 212, 214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197,196, 195, 192, 190, 187, 185, 183, 182, 181, 176, 175, 173, 172, 165,164, 163, 161, 159, 155, 151, 149, 147, 145, 144, 143, 136, 132, 129,127, 125, 116, 115, 109, 108, 106, 105, 104, 100, 97, 96, 94, 92, 90,88, 86, 85, 79, 75, 69, 65, 63, 62, 59, 57, 56, 54, 52, 51, 50, 48, 44,40, 39, 38, 37, 36, 35, 34, 33, 31, 29, 27, 25, 24, 21, 20, 19, 18, 17,16, 11, 9, 8, 7, 6, 4, 3, 203, 193, 191, 189, 188, 184, 178, 177, 174,169, 160, 156, 150, 146, 140, 134, 131, 126, 117, 113, 112, 103, 101,98, 95, 91, 87, 80, 73, 72, 67, 66, 61, 53, 49, 47, 42, 41, 32, 30, 28,23, 14, 13, 12, 2, 1, 0, 204, 194, 186, 179, 170, 157, 152, 148, 141,137, 135, 133, 118, 114, 110, 102, 99, 93, 89, 81, 76, 74, 68, 60, 58,55, 43, 15, 205, 180, 171, 162, 158, 153, 142, 138, 128, 119, 111, 107,82, 77, 22, 5, 206, 167, 139, 121, 120, 84, 78, 70, 64, 45, 26, 10, 208,166, 130, 123, 122, 71, 210, 83, 46, 213, 124, 154, 168, 200, 201, 202,207, 209, 211, 212, 214, 215, 216, 217, 218 200 20 0x191513 2, 3, 6, 10,11, 15, 17, 18, 19, 21, 26, 27, 31, 32, 33, 36, 38, 40, 42, 44, 45, 48,49, 50, 51, 53, 54, 58, 61, 62, 68, 69, 72, 73, 78, 80, 81, 83, 85, 88,89, 90, 93, 94, 95, 96, 100, 101, 103, 105, 107, 108, 110, 111, 112,114, 115, 116, 118, 121, 124, 126, 127, 130, 132, 133, 134, 139, 140,141, 142, 143, 144, 146, 148, 149, 153, 154, 155, 156, 158, 160, 161,164, 169, 176, 178, 179, 180, 181, 184, 185, 186, 188, 189, 193, 195,197, 198, 199, 200, 0, 4, 7, 12, 16, 20, 22, 28, 34, 37, 39, 41, 43, 46,52, 55, 59, 63, 70, 74, 79, 82, 84, 86, 91, 97, 102, 104, 106, 109, 113,117, 119, 122, 125, 128, 131, 135, 145, 147, 150, 157, 159, 162, 165,170, 177, 182, 187, 190, 194, 196, 201, 1, 5, 8, 13, 23, 29, 35, 47, 56,60, 64, 71, 75, 87, 92, 98, 120, 123, 129, 136, 151, 163, 166, 171, 183,191, 202, 9, 14, 24, 30, 57, 65, 76, 99, 137, 152, 167, 172, 192, 203,25, 66, 77, 138, 168, 173, 204, 67, 174, 205, 175, 206, 207, 208, 209,210, 211, 212, 213, 214, 215, 216, 217, 218, 219 200 20 0x191513 199,198, 197, 195, 193, 189, 188, 186, 185, 184, 181, 180, 179, 178, 176,169, 164, 161, 160, 158, 156, 155, 154, 153, 149, 148, 146, 144, 143,142, 141, 140, 139, 134, 133, 132, 130, 127, 126, 124, 121, 118, 116,115, 114, 112, 111, 110, 108, 107, 105, 103, 101, 100, 96, 95, 94, 93,90, 89, 88, 85, 83, 81, 80, 78, 73, 72, 69, 68, 62, 61, 58, 54, 53, 51,50, 49, 48, 45, 44, 42, 40, 38, 36, 33, 32, 31, 27, 26, 21, 19, 18, 17,15, 11, 10, 6, 3, 2, 200, 196, 194, 190, 187, 182, 177, 170, 165, 162,159, 157, 150, 147, 145, 135, 131, 128, 125, 122, 119, 117, 113, 109,106, 104, 102, 97, 91, 86, 84, 82, 79, 74, 70, 63, 59, 55, 52, 46, 43,41, 39, 37, 34, 28, 22, 20, 16, 12, 7, 4, 0, 201, 191, 183, 171, 166,163, 151, 136, 129, 123, 120, 98, 92, 87, 75, 71, 64, 60, 56, 47, 35,29, 23, 13, 8, 5, 1, 202, 192, 172, 167, 152, 137, 99, 76, 65, 57, 30,24, 14, 9, 203, 173, 168, 138, 77, 66, 25, 204, 174, 67, 205, 175, 206,207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 200 210x2E2A69 1, 5, 6, 8, 9, 10, 12, 14, 15, 17, 19, 21, 23, 26, 27, 28, 29,30, 32, 33, 35, 39, 41, 47, 49, 51, 52, 53, 55, 58, 59, 60, 61, 63, 66,69, 72, 74, 76, 78, 79, 83, 87, 88, 89, 94, 96, 97, 101, 103, 105, 108,109, 110, 111, 113, 114, 118, 125, 127, 131, 133, 134, 135, 136, 137,138, 141, 142, 147, 150, 151, 156, 159, 160, 162, 163, 164, 168, 170,171, 172, 173, 174, 177, 180, 181, 182, 184, 188, 190, 195, 197, 200, 0,2, 7, 11, 13, 16, 18, 20, 22, 24, 31, 34, 36, 40, 42, 48, 50, 54, 56,62, 64, 67, 70, 73, 75, 77, 80, 84, 90, 95, 98, 102, 104, 106, 112, 115,119, 126, 128, 132, 139, 143, 148, 152, 157, 161, 165, 169, 175, 178,183, 185, 189, 191, 196, 198, 201, 3, 25, 37, 43, 57, 65, 68, 71, 81,85, 91, 99, 107, 116, 120, 129, 140, 144, 149, 153, 158, 166, 176, 179,186, 192, 199, 202, 4, 38, 44, 82, 86, 92, 100, 117, 121, 130, 145, 154,167, 187, 193, 203, 45, 93, 122, 146, 155, 194, 204, 46, 123, 205, 124,206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219,220 200 21 0x2E2A69 197, 195, 190, 188, 184, 182, 181, 180, 177, 174,173, 172, 171, 170, 168, 164, 163, 162, 160, 159, 156, 151, 150, 147,142, 141, 138, 137, 136, 135, 134, 133, 131, 127, 125, 118, 114, 113,111, 110, 109, 108, 105, 103, 101, 97, 96, 94, 89, 88, 87, 83, 79, 78,76, 74, 72, 69, 66, 63, 61, 60, 59, 58, 55, 53, 52, 51, 49, 47, 41, 39,35, 33, 32, 30, 29, 28, 27, 26, 23, 21, 19, 17, 15, 14, 12, 10, 9, 8, 6,5, 1, 200, 198, 196, 191, 189, 185, 183, 178, 175, 169, 165, 161, 157,152, 148, 143, 139, 132, 128, 126, 119, 115, 112, 106, 104, 102, 98, 95,90, 84, 80, 77, 75, 73, 70, 67, 64, 62, 56, 54, 50, 48, 42, 40, 36, 34,31, 24, 22, 20, 18, 16, 13, 11, 7, 2, 0, 201, 199, 192, 186, 179, 176,166, 158, 153, 149, 144, 140, 129, 120, 116, 107, 99, 91, 85, 81, 71,68, 65, 57, 43, 37, 25, 3, 202, 193, 187, 167, 154, 145, 130, 121, 117,100, 92, 86, 82, 44, 38, 4, 203, 194, 155, 146, 122, 93, 45, 204, 123,46, 205, 124, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216,217, 218, 219, 220 200 22 0x552A55 1, 2, 3, 4, 12, 14, 15, 17, 19, 20,22, 24, 27, 30, 34, 35, 36, 37, 38, 39, 40, 41, 44, 45, 48, 49, 50, 51,52, 56, 57, 58, 60, 61, 62, 65, 67, 68, 69, 72, 74, 75, 76, 80, 81, 82,84, 85, 86, 87, 92, 93, 95, 102, 105, 106, 107, 108, 110, 111, 113, 116,117, 119, 121, 122, 125, 129, 130, 131, 132, 134, 136, 138, 141, 142,147, 148, 149, 150, 152, 159, 161, 165, 169, 170, 171, 172, 174, 175,180, 182, 183, 185, 189, 190, 191, 192, 198, 200, 5, 13, 16, 18, 21, 23,25, 28, 31, 42, 46, 53, 59, 63, 66, 70, 73, 77, 83, 88, 94, 96, 103,109, 112, 114, 118, 120, 123, 126, 133, 135, 137, 139, 143, 151, 153,160, 162, 166, 173, 176, 181, 184, 186, 193, 199, 201, 6, 26, 29, 32,43, 47, 54, 64, 71, 78, 89, 97, 104, 115, 124, 127, 140, 144, 154, 163,167, 177, 187, 194, 202, 0, 7, 33, 55, 79, 90, 98, 128, 145, 155, 164,168, 178, 188, 195, 203, 8, 91, 99, 146, 156, 179, 196, 204, 9, 100,157, 197, 205, 10, 101, 158, 206, 11, 207, 208, 209, 210, 211, 212, 213,214, 215, 216, 217, 218, 219, 220, 221 200 22 0x552A55 198, 192, 191,190, 189, 185, 183, 182, 180, 175, 174, 172, 171, 170, 169, 165, 161,159, 152, 150, 149, 148, 147, 142, 141, 138, 136, 134, 132, 131, 130,129, 125, 122, 121, 119, 117, 116, 113, 111, 110, 108, 107, 106, 105,102, 95, 93, 92, 87, 86, 85, 84, 82, 81, 80, 76, 75, 74, 72, 69, 68, 67,65, 62, 61, 60, 58, 57, 56, 52, 51, 50, 49, 48, 45, 44, 41, 40, 39, 38,37, 36, 35, 34, 30, 27, 24, 22, 20, 19, 17, 15, 14, 12, 4, 3, 2, 1, 200,199, 193, 186, 184, 181, 176, 173, 166, 162, 160, 153, 151, 143, 139,137, 135, 133, 126, 123, 120, 118, 114, 112, 109, 103, 96, 94, 88, 83,77, 73, 70, 66, 63, 59, 53, 46, 42, 31, 28, 25, 23, 21, 18, 16, 13, 5,201, 194, 187, 177, 167, 163, 154, 144, 140, 127, 124, 115, 104, 97, 89,78, 71, 64, 54, 47, 43, 32, 29, 26, 6, 202, 195, 188, 178, 168, 164,155, 145, 128, 98, 90, 79, 55, 33, 7, 0, 203, 196, 179, 156, 146, 99,91, 8, 204, 197, 157, 100, 9, 205, 158, 101, 10, 206, 11, 207, 208, 209,210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 200 230x86F4A1 1, 3, 4, 5, 11, 12, 13, 14, 18, 20, 23, 24, 25, 28, 30, 31, 32,33, 37, 39, 42, 45, 46, 47, 49, 50, 51, 53, 55, 57, 59, 60, 61, 64, 65,67, 69, 70, 71, 72, 73, 74, 75, 77, 80, 83, 84, 85, 86, 87, 88, 89, 90,93, 94, 99, 101, 102, 104, 106, 109, 111, 112, 113, 115, 116, 119, 121,123, 124, 133, 134, 135, 137, 139, 140, 141, 142, 144, 145, 148, 149,152, 153, 154, 157, 159, 162, 164, 166, 168, 169, 175, 176, 178, 179,180, 181, 182, 187, 188, 193, 195, 200, 0, 2, 6, 15, 19, 21, 26, 29, 34,38, 40, 43, 48, 52, 54, 56, 58, 62, 66, 68, 76, 78, 81, 91, 95, 100,103, 105, 107, 110, 114, 117, 120, 122, 125, 136, 138, 143, 146, 150,155, 158, 160, 163, 165, 167, 170, 177, 183, 189, 194, 196, 201, 7, 16,22, 27, 35, 41, 44, 63, 79, 82, 92, 96, 108, 118, 126, 147, 151, 156,161, 171, 184, 190, 197, 202, 8, 17, 36, 97, 127, 172, 185, 191, 198,203, 9, 98, 128, 173, 186, 192, 199, 204, 10, 129, 174, 205, 130, 206,131, 207, 132, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218,219, 220, 221, 222 200 23 0x86F4A1 195, 193, 188, 187, 182, 181, 180,179, 178, 176, 175, 169, 168, 166, 164, 162, 159, 157, 154, 153, 152,149, 148, 145, 144, 142, 141, 140, 139, 137, 135, 134, 133, 124, 123,121, 119, 116, 115, 113, 112, 111, 109, 106, 104, 102, 101, 99, 94, 93,90, 89, 88, 87, 86, 85, 84, 83, 80, 77, 75, 74, 73, 72, 71, 70, 69, 67,65, 64, 61, 60, 59, 57, 55, 53, 51, 50, 49, 47, 46, 45, 42, 39, 37, 33,32, 31, 30, 28, 25, 24, 23, 20, 18, 14, 13, 12, 11, 5, 4, 3, 1, 200,196, 194, 189, 183, 177, 170, 167, 165, 163, 160, 158, 155, 150, 146,143, 138, 136, 125, 122, 120, 117, 114, 110, 107, 105, 103, 100, 95, 91,81, 78, 76, 68, 66, 62, 58, 56, 54, 52, 48, 43, 40, 38, 34, 29, 26, 21,19, 15, 6, 2, 0, 201, 197, 190, 184, 171, 161, 156, 151, 147, 126, 118,108, 96, 92, 82, 79, 63, 44, 41, 35, 27, 22, 16, 7, 202, 198, 191, 185,172, 127, 97, 36, 17, 8, 203, 199, 192, 186, 173, 128, 98, 9, 204, 174,129, 10, 205, 130, 206, 131, 207, 132, 208, 209, 210, 211, 212, 213,214, 215, 216, 217, 218, 219, 220, 221, 222 200 24 0x1D11A9B 0, 2, 3, 5,6, 8, 11, 12, 13, 16, 19, 20, 22, 24, 28, 32, 33, 35, 37, 38, 39, 40,41, 42, 44, 46, 47, 49, 50, 54, 55, 57, 59, 60, 62, 64, 67, 69, 74, 79,80, 84, 85, 86, 88, 91, 94, 102, 105, 109, 110, 111, 113, 114, 116, 118,119, 121, 122, 125, 126, 127, 129, 130, 131, 132, 136, 137, 141, 142,143, 147, 148, 149, 151, 153, 155, 158, 161, 164, 166, 168, 170, 171,173, 175, 178, 179, 180, 182, 183, 186, 187, 189, 192, 194, 198, 199,200, 1, 4, 7, 9, 14, 17, 21, 23, 25, 29, 34, 36, 43, 45, 48, 51, 56, 58,61, 63, 65, 68, 70, 75, 81, 87, 89, 92, 95, 103, 106, 112, 115, 117,120, 123, 128, 133, 138, 144, 150, 152, 154, 156, 159, 162, 165, 167,169, 172, 174, 176, 181, 184, 188, 190, 193, 195, 201, 10, 15, 18, 26,30, 52, 66, 71, 76, 82, 90, 93, 96, 104, 107, 124, 134, 139, 145, 157,160, 163, 177, 185, 191, 196, 202, 27, 31, 53, 72, 77, 83, 97, 108, 135,140, 146, 197, 203, 73, 78, 98, 204, 99, 205, 100, 206, 101, 207, 208,209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222,223 200 24 0x1D11A9B 199, 198, 194, 192, 189, 187, 186, 183, 182, 180,179, 178, 175, 173, 171, 170, 168, 166, 164, 161, 158, 155, 153, 151,149, 148, 147, 143, 142, 141, 137, 136, 132, 131, 130, 129, 127, 126,125, 122, 121, 119, 118, 116, 114, 113, 111, 110, 109, 105, 102, 94, 91,88, 86, 85, 84, 80, 79, 74, 69, 67, 64, 62, 60, 59, 57, 55, 54, 50, 49,47, 46, 44, 42, 41, 40, 39, 38, 37, 35, 33, 32, 28, 24, 22, 20, 19, 16,13, 12, 11, 8, 6, 5, 3, 2, 0, 200, 195, 193, 190, 188, 184, 181, 176,174, 172, 169, 167, 165, 162, 159, 156, 154, 152, 150, 144, 138, 133,128, 123, 120, 117, 115, 112, 106, 103, 95, 92, 89, 87, 81, 75, 70, 68,65, 63, 61, 58, 56, 51, 48, 45, 43, 36, 34, 29, 25, 23, 21, 17, 14, 9,7, 4, 1, 201, 196, 191, 185, 177, 163, 160, 157, 145, 139, 134, 124,107, 104, 96, 93, 90, 82, 76, 71, 66, 52, 30, 26, 18, 15, 10, 202, 197,146, 140, 135, 108, 97, 83, 77, 72, 53, 31, 27, 203, 98, 78, 73, 204,99, 205, 100, 206, 101, 207, 208, 209, 210, 211, 212, 213, 214, 215,216, 217, 218, 219, 220, 221, 222, 223 1000 11 0x94F 0, 1, 4, 5, 6, 8,13, 14, 15, 17, 18, 22, 24, 26, 29, 30, 32, 33, 34, 38, 39, 40, 43, 44,47, 50, 52, 53, 58, 59, 62, 63, 65, 67, 72, 73, 75, 76, 78, 79, 82, 85,86, 88, 89, 90, 91, 95, 97, 100, 104, 105, 108, 112, 113, 115, 116, 118,124, 126, 127, 128, 129, 130, 132, 133, 134, 135, 141, 142, 145, 147,148, 149, 151, 153, 154, 156, 159, 161, 164, 167, 168, 169, 170, 173,175, 176, 177, 181, 185, 189, 191, 193, 194, 195, 196, 198, 200, 202,203, 205, 207, 211, 212, 213, 214, 215, 217, 218, 222, 223, 224, 228,230, 231, 232, 233, 234, 235, 236, 237, 239, 240, 241, 243, 245, 246,247, 248, 250, 251, 252, 255, 256, 267, 270, 272, 273, 275, 279, 280,281, 282, 285, 288, 289, 290, 292, 295, 297, 299, 300, 302, 303, 306,307, 309, 314, 320, 322, 324, 325, 330, 335, 336, 343, 346, 347, 348,349, 350, 351, 352, 353, 356, 357, 358, 359, 360, 362, 364, 366, 369,370, 371, 372, 373, 376, 377, 378, 380, 385, 386, 387, 389, 390, 394,396, 398, 401, 402, 404, 405, 406, 410, 411, 412, 415, 416, 419, 422,424, 425, 430, 431, 434, 435, 437, 439, 444, 445, 447, 448, 450, 451,454, 457, 458, 460, 461, 462, 463, 467, 469, 472, 476, 477, 480, 484,485, 487, 488, 490, 496, 498, 499, 500, 501, 502, 504, 505, 506, 507,513, 514, 517, 519, 520, 521, 523, 525, 526, 528, 531, 533, 536, 539,540, 541, 542, 545, 547, 548, 549, 553, 557, 561, 563, 565, 566, 567,568, 570, 572, 574, 575, 577, 579, 583, 584, 585, 586, 587, 589, 590,594, 595, 596, 600, 602, 603, 604, 605, 606, 607, 608, 609, 611, 612,613, 615, 617, 618, 619, 620, 622, 623, 624, 627, 628, 639, 642, 644,645, 647, 651, 652, 653, 654, 657, 660, 661, 662, 664, 667, 669, 671,672, 674, 675, 678, 679, 681, 686, 692, 694, 696, 697, 702, 707, 708,715, 718, 719, 720, 721, 722, 723, 724, 725, 728, 729, 730, 731, 732,734, 736, 738, 741, 742, 743, 744, 745, 748, 749, 750, 752, 757, 758,759, 761, 762, 766, 768, 770, 773, 774, 776, 777, 778, 782, 783, 784,787, 788, 791, 794, 796, 797, 802, 803, 806, 807, 809, 811, 816, 817,819, 820, 822, 823, 826, 829, 830, 832, 833, 834, 835, 839, 841, 844,848, 849, 852, 856, 857, 859, 860, 862, 868, 870, 871, 872, 873, 874,876, 877, 878, 879, 885, 886, 889, 891, 892, 893, 895, 897, 898, 900,903, 905, 908, 911, 912, 913, 914, 917, 919, 920, 921, 925, 929, 933,935, 937, 938, 939, 940, 942, 944, 946, 947, 949, 951, 955, 956, 957,958, 959, 961, 962, 966, 967, 968, 972, 974, 975, 976, 977, 978, 979,980, 981, 983, 984, 985, 987, 989, 990, 991, 992, 994, 995, 996, 999,1000, 2, 7, 9, 16, 19, 23, 25, 27, 31, 35, 41, 45, 48, 51, 54, 60, 64,66, 68, 74, 77, 80, 83, 87, 92, 96, 98, 101, 106, 109, 114, 117, 119,125, 131, 136, 143, 146, 150, 152, 155, 157, 160, 162, 165, 171, 174,178, 182, 186, 190, 192, 197, 199, 201, 204, 206, 208, 216, 219, 225,229, 238, 242, 244, 249, 253, 257, 268, 271, 274, 276, 283, 286, 291,293, 296, 298, 301, 304, 308, 310, 315, 321, 323, 326, 331, 337, 344,354, 361, 363, 365, 367, 374, 379, 381, 388, 391, 395, 397, 399, 403,407, 413, 417, 420, 423, 426, 432, 436, 438, 440, 446, 449, 452, 455,459, 464, 468, 470, 473, 478, 481, 486, 489, 491, 497, 503, 508, 515,518, 522, 524, 527, 529, 532, 534, 537, 543, 546, 550, 554, 558, 562,564, 569, 571, 573, 576, 578, 580, 588, 591, 597, 601, 610, 614, 616,621, 625, 629, 640, 643, 646, 648, 655, 658, 663, 665, 668, 670, 673,676, 680, 682, 687, 693, 695, 698, 703, 709, 716, 726, 733, 735, 737,739, 746, 751, 753, 760, 763, 767, 769, 771, 775, 779, 785, 789, 792,795, 798, 804, 808, 810, 812, 818, 821, 824, 827, 831, 836, 840, 842,845, 850, 853, 858, 861, 863, 869, 875, 880, 887, 890, 894, 896, 899,901, 904, 906, 909, 915, 918, 922, 926, 930, 934, 936, 941, 943, 945,948, 950, 952, 960, 963, 969, 973, 982, 986, 988, 993, 997, 1001, 3, 10,20, 28, 36, 42, 46, 49, 55, 61, 69, 81, 84, 93, 99, 102, 107, 110, 120,137, 144, 158, 163, 166, 172, 179, 183, 187, 209, 220, 226, 254, 258,269, 277, 284, 287, 294, 305, 311, 316, 327, 332, 338, 345, 355, 368,375, 382, 392, 400, 408, 414, 418, 421, 427, 433, 441, 453, 456, 465,471, 474, 479, 482, 492, 509, 516, 530, 535, 538, 544, 551, 555, 559,581, 592, 598, 626, 630, 641, 649, 656, 659, 666, 677, 683, 688, 699,704, 710, 717, 727, 740, 747, 754, 764, 772, 780, 786, 790, 793, 799,805, 813, 825, 828, 837, 843, 846, 851, 854, 864, 881, 888, 902, 907,910, 916, 923, 927, 931, 953, 964, 970, 998, 1002, 11, 21, 37, 56, 70,94, 103, 111, 121, 138, 180, 184, 188, 210, 221, 227, 259, 278, 312,317, 328, 333, 339, 383, 393, 409, 428, 442, 466, 475, 483, 493, 510,552, 556, 560, 582, 593, 599, 631, 650, 684, 689, 700, 705, 711, 755,765, 781, 800, 814, 838, 847, 855, 865, 882, 924, 928, 932, 954, 965,971, 1003, 12, 57, 71, 122, 139, 260, 313, 318, 329, 334, 340, 384, 429,443, 494, 511, 632, 685, 690, 701, 706, 712, 756, 801, 815, 866, 883,1004, 123, 140, 261, 319, 341, 495, 512, 633, 691, 713, 867, 884, 1005,262, 342, 634, 714, 1006, 263, 635, 1007, 264, 636, 1008, 265, 637,1009, 266, 638, 1010 1000 11 0x94F 999, 996, 995, 994, 992, 991, 990,989, 987, 985, 984, 983, 981, 980, 979, 978, 977, 976, 975, 974, 972,968, 967, 966, 962, 961, 959, 958, 957, 956, 955, 951, 949, 947, 946,944, 942, 940, 939, 938, 937, 935, 933, 929, 925, 921, 920, 919, 917,914, 913, 912, 911, 908, 905, 903, 900, 898, 897, 895, 893, 892, 891,889, 886, 885, 879, 878, 877, 876, 874, 873, 872, 871, 870, 868, 862,860, 859, 857, 856, 852, 849, 848, 844, 841, 839, 835, 834, 833, 832,830, 829, 826, 823, 822, 820, 819, 817, 816, 811, 809, 807, 806, 803,802, 797, 796, 794, 791, 788, 787, 784, 783, 782, 778, 777, 776, 774,773, 770, 768, 766, 762, 761, 759, 758, 757, 752, 750, 749, 748, 745,744, 743, 742, 741, 738, 736, 734, 732, 731, 730, 729, 728, 725, 724,723, 722, 721, 720, 719, 718, 715, 708, 707, 702, 697, 696, 694, 692,686, 681, 679, 678, 675, 674, 672, 671, 669, 667, 664, 662, 661, 660,657, 654, 653, 652, 651, 647, 645, 644, 642, 639, 628, 627, 624, 623,622, 620, 619, 618, 617, 615, 613, 612, 611, 609, 608, 607, 606, 605,604, 603, 602, 600, 596, 595, 594, 590, 589, 587, 586, 585, 584, 583,579, 577, 575, 574, 572, 570, 568, 567, 566, 565, 563, 561, 557, 553,549, 548, 547, 545, 542, 541, 540, 539, 536, 533, 531, 528, 526, 525,523, 521, 520, 519, 517, 514, 513, 507, 506, 505, 504, 502, 501, 500,499, 498, 496, 490, 488, 487, 485, 484, 480, 477, 476, 472, 469, 467,463, 462, 461, 460, 458, 457, 454, 451, 450, 448, 447, 445, 444, 439,437, 435, 434, 431, 430, 425, 424, 422, 419, 416, 415, 412, 411, 410,406, 405, 404, 402, 401, 398, 396, 394, 390, 389, 387, 386, 385, 380,378, 377, 376, 373, 372, 371, 370, 369, 366, 364, 362, 360, 359, 358,357, 356, 353, 352, 351, 350, 349, 348, 347, 346, 343, 336, 335, 330,325, 324, 322, 320, 314, 309, 307, 306, 303, 302, 300, 299, 297, 295,292, 290, 289, 288, 285, 282, 281, 280, 279, 275, 273, 272, 270, 267,256, 255, 252, 251, 250, 248, 247, 246, 245, 243, 241, 240, 239, 237,236, 235, 234, 233, 232, 231, 230, 228, 224, 223, 222, 218, 217, 215,214, 213, 212, 211, 207, 205, 203, 202, 200, 198, 196, 195, 194, 193,191, 189, 185, 181, 177, 176, 175, 173, 170, 169, 168, 167, 164, 161,159, 156, 154, 153, 151, 149, 148, 147, 145, 142, 141, 135, 134, 133,132, 130, 129, 128, 127, 126, 124, 118, 116, 115, 113, 112, 108, 105,104, 100, 97, 95, 91, 90, 89, 88, 86, 85, 82, 79, 78, 76, 75, 73, 72,67, 65, 63, 62, 59, 58, 53, 52, 50, 47, 44, 43, 40, 39, 38, 34, 33, 32,30, 29, 26, 24, 22, 18, 17, 15, 14, 13, 8, 6, 5, 4, 1, 0, 1000, 997,993, 988, 986, 982, 973, 969, 963, 960, 952, 950, 948, 945, 943, 941,936, 934, 930, 926, 922, 918, 915, 909, 906, 904, 901, 899, 896, 894,890, 887, 880, 875, 869, 863, 861, 858, 853, 850, 845, 842, 840, 836,831, 827, 824, 821, 818, 812, 810, 808, 804, 798, 795, 792, 789, 785,779, 775, 771, 769, 767, 763, 760, 753, 751, 746, 739, 737, 735, 733,726, 716, 709, 703, 698, 695, 693, 687, 682, 680, 676, 673, 670, 668,665, 663, 658, 655, 648, 646, 643, 640, 629, 625, 621, 616, 614, 610,601, 597, 591, 588, 580, 578, 576, 573, 571, 569, 564, 562, 558, 554,550, 546, 543, 537, 534, 532, 529, 527, 524, 522, 518, 515, 508, 503,497, 491, 489, 486, 481, 478, 473, 470, 468, 464, 459, 455, 452, 449,446, 440, 438, 436, 432, 426, 423, 420, 417, 413, 407, 403, 399, 397,395, 391, 388, 381, 379, 374, 367, 365, 363, 361, 354, 344, 337, 331,326, 323, 321, 315, 310, 308, 304, 301, 298, 296, 293, 291, 286, 283,276, 274, 271, 268, 257, 253, 249, 244, 242, 238, 229, 225, 219, 216,208, 206, 204, 201, 199, 197, 192, 190, 186, 182, 178, 174, 171, 165,162, 160, 157, 155, 152, 150, 146, 143, 136, 131, 125, 119, 117, 114,109, 106, 101, 98, 96, 92, 87, 83, 80, 77, 74, 68, 66, 64, 60, 54, 51,48, 45, 41, 35, 31, 27, 25, 23, 19, 16, 9, 7, 2, 1001, 998, 970, 964,953, 931, 927, 923, 916, 910, 907, 902, 888, 881, 864, 854, 851, 846,843, 837, 828, 825, 813, 805, 799, 793, 790, 786, 780, 772, 764, 754,747, 740, 727, 717, 710, 704, 699, 688, 683, 677, 666, 659, 656, 649,641, 630, 626, 598, 592, 581, 559, 555, 551, 544, 538, 535, 530, 516,509, 492, 482, 479, 474, 471, 465, 456, 453, 441, 433, 427, 421, 418,414, 408, 400, 392, 382, 375, 368, 355, 345, 338, 332, 327, 316, 311,305, 294, 287, 284, 277, 269, 258, 254, 226, 220, 209, 187, 183, 179,172, 166, 163, 158, 144, 137, 120, 110, 107, 102, 99, 93, 84, 81, 69,61, 55, 49, 46, 42, 36, 28, 20, 10, 3, 1002, 971, 965, 954, 932, 928,924, 882, 865, 855, 847, 838, 814, 800, 781, 765, 755, 711, 705, 700,689, 684, 650, 631, 599, 593, 582, 560, 556, 552, 510, 493, 483, 475,466, 442, 428, 409, 393, 383, 339, 333, 328, 317, 312, 278, 259, 227,221, 210, 188, 184, 180, 138, 121, 111, 103, 94, 70, 56, 37, 21, 11,1003, 883, 866, 815, 801, 756, 712, 706, 701, 690, 685, 632, 511, 494,443, 429, 384, 340, 334, 329, 318, 313, 260, 139, 122, 71, 57, 12, 1004,884, 867, 713, 691, 633, 512, 495, 341, 319, 261, 140, 123, 1005, 714,634, 342, 262, 1006, 635, 263, 1007, 636, 264, 1008, 637, 265, 1009,638, 266, 1010 22 3 0xD 1, 4, 5, 6, 8, 11, 12, 13, 0, 19, 2, 3, 15, 18,20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24 22 3 0xD 4, 5, 6, 8, 1, 12, 11,13, 2, 19, 0, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24 22 30xD 1, 4, 5, 6, 8, 12, 11, 13, 0, 19, 2, 3, 15, 18, 20, 7, 9, 22, 10,21, 16, 14, 23, 17, 24 22 3 0xD 1, 4, 5, 6, 12, 11, 13, 8, 0, 19, 2, 3,15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24

For example, L=19, the polynomial is 0xA2B79, and the interleavingsequence π1={0, 1, 2, 5, 6, 7, 10, 11, 13, 14, 18, 19, 20, 22, 23, 24,26, 31, 33, 35, 37, 39, 42, 44, 45, 47, 51, 52, 55, 56, 57, 58, 60, 61,62, 64, 67, 69, 70, 72, 73, 76, 85, 86, 89, 90, 93, 94, 100, 103, 104,105, 107, 109, 110, 112, 113, 125, 127, 128, 129, 130, 131, 133, 134,137, 140, 144, 145, 148, 149, 152, 159, 161, 162, 163, 166, 169, 173,175, 178, 182, 183, 186, 187, 189, 195, 196, 197, 200, 3, 8, 12, 15, 21,25, 27, 32, 34, 36, 38, 40, 43, 46, 48, 53, 59, 63, 65, 68, 71, 74, 77,87, 91, 95, 101, 106, 108, 111, 114, 126, 132, 135, 138, 141, 146, 150,153, 160, 164, 167, 170, 174, 176, 179, 184, 188, 190, 198, 201, 4, 9,16, 28, 41, 49, 54, 66, 75, 78, 88, 92, 96, 102, 115, 136, 139, 142,147, 151, 154, 165, 168, 171, 177, 180, 185, 191, 199, 202, 17, 29, 50,79, 97, 116, 143, 155, 172, 181, 192, 203, 30, 80, 98, 117, 156, 193,204, 81, 99, 118, 157, 194, 205, 82, 119, 158, 206, 83, 120, 207, 84,121, 208, 122, 209, 123, 210, 124, 211, 212, 213, 214, 215, 216, 217,218}. For example, if a length A of a current information bit sequenceis equal to 64, a bit sequence obtained after CRC encoding is {b₀, b₁, .. . , b₈₂}. A currently required interleaving sequence π1′={1, 4, 8, 9,12, 13, 16, 23, 25, 26, 27, 30, 33, 37, 39, 42, 46, 47, 50, 51, 53, 59,60, 61, 64, 2, 5, 10, 14, 17, 24, 28, 31, 34, 38, 40, 43, 48, 52, 54,62, 65, 0, 3, 6, 11, 15, 18, 29, 32, 35, 41, 44, 49, 55, 63, 66, 7, 19,36, 45, 56, 67, 20, 57, 68, 21, 58, 69, 22, 70, 71, 72, 73, 74, 75, 76,77, 78, 79, 80, 81, 82} is extracted from the interleaving sequence π1based on S202. The sequence {b₀, b₁, . . . , b₈₂} is interleaved basedon S203, to obtain {c₀, c₁, . . . , c₈₂}={b₁, b₄, b₈, b₉, b₁₂, b₁₃, b₁₆,b₂₃, b₂₅, b₂₆, b₂₇, b₃₀, b₃₃, b₃₇, b₃₉, b₄₂, b₄₆, b₄₇, b₅₀, b₅₁, b₅₃,b₅₉, b₆₀, b₆₁, b₆₄, b₂, b₅, b₀, b₁₄, b₁₇, b₂₄, b₂₈, b₃₁, b₃₄, b₃₈, b₄₀,b₄₃, b₄₈, b₅₂, b₅₄, b₆₂, b₆₅, b₀, b₃, b₆, b₁₁, b₁₅, b₁₈, b₂₉, b₃₂, b₃₅,b₄₁, b₄₄, b₄₉, b₅₅, b₆₃, b₆₆, b₇, b₁₉, b₃₆, b₄₅, b₅₆, b₆₇, b₂₀, b₅₇,b₆₈, b₂₁, b₅₈, b₆₉, b₂₂, b₇₀, b₇₁, b₇₂, b₇₃, b₇₄, b₇₅, b₇₆, b₇₇, b₇₈,b₇₉, b₈₀, b₈₁, b₈₂}.

In Table 1, when K_(max)=200, L=19, and the CRC polynomial is 0xA2B79,there are six corresponding interleaving sequences for whichnatural-order numbering is used. A better early termination effect isachieved when a first interleaving sequence, a third interleavingsequence, or a fifth interleaving sequence is used for a low code-ratepolar code. A better early termination effect is achieved when a secondinterleaving sequence, a fourth interleaving sequence, or a sixthinterleaving sequence is used for a high code-rate polar code. A betterearly termination effect is achieved when a first interleaving sequenceor a second interleaving sequence is used for polar code SC decoding. Abetter early termination effect is achieved when a third interleavingsequence or a fourth interleaving sequence is used for a polar code witha long code length. A better early termination effect is achieved when afifth interleaving sequence or a sixth interleaving sequence is used fora polar code with a short code length.

When K_(max)=200, L=20, and the CRC polynomial is 0x191513, there aretwo corresponding interleaving sequences for which natural-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a low code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a high code-rate polar code.

When K_(max)=200, L=21, and the CRC polynomial is 0x2E2A69, there aretwo corresponding interleaving sequences for which natural-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a low code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a high code-rate polar code.

When K_(max)=200, L=22, and the CRC polynomial is 0x552A55, there aretwo corresponding interleaving sequences for which natural-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a low code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a high code-rate polar code.

When K_(max)=200, L=23, and the CRC polynomial is 0x86F4A1, there aretwo corresponding interleaving sequences for which natural-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a low code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a high code-rate polar code.

When K_(max)=200, L=24, and the CRC polynomial is 0x1D11A9B, there aretwo corresponding interleaving sequences for which natural-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a low code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a high code-rate polar code.

When K_(max)1000, L=11, and the CRC polynomial is 0x94F, there are twocorresponding interleaving sequences for which natural-order numberingis used. A better early termination effect is achieved when a firstinterleaving sequence is used for a low code-rate polar code. A betterearly termination effect is achieved when a second interleaving sequenceis used for a high code-rate polar code.

When K_(max)22, L=3, and the CRC polynomial is 0xD, there are fourcorresponding interleaving sequences for which natural-order numberingis used. A better early termination effect is achieved when a firstinterleaving sequence is used for a polar code whose code length is 32after encoding. A better early termination effect is achieved when asecond interleaving sequence is used for a polar code whose code lengthis 64 after encoding. A better early termination effect is achieved whena third interleaving sequence is used for a polar code whose code lengthis 128 after encoding. A better early termination effect is achievedwhen a fourth interleaving sequence is used for a polar code whose codelength is 256 after encoding.

It should be noted that hexadecimal bit-reversed and explicit +1notation is used for the CRC polynomial in Table 1 and a CRC polynomialin the following Table 2. For example, a polynomial 0xA2B79 correspondsto a binary polynomial (1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0,0, 1, 0, 1), and corresponds to a polynomialD̂9+D̂6+D̂15+D̂14+D̂3+D̂11+D̂10+D̂8+D̂6+D̂2+1.

FIG. 5 is a schematic flowchart of an encoding method according to thisapplication. In this embodiment, for example, an interleaving sequenceused for an interleaving operation is the first interleaving sequenceobtained based on the preset rule in Manner 2, a maximum-lengthinterleaving sequence used for distributed CRC encoding is a sequence π2for which reverse-order numbering is used, a maximum information bitlength corresponding to π2 is K_(max), a CRC polynomial is g, and a CRCbit quantity is L. In other words, a CRC length is L. It is assumed thatA to-be-encoded information bits are {a₀, a₁, . . . , a_(A−1)}, and theinformation bit quantity A≤K_(max). This embodiment is performed by atransmit end (an encoder). As shown in FIG. 5, the method in thisembodiment includes the following steps.

S301. Perform CRC encoding on A to-be-encoded information bits, toobtain a first bit sequence {b₀, b₁, . . . , b_(A+L-1)}.

{b₀, b₁, . . . , b_(A−1)} are A information bits, and {b_(A), b_(A+1), .. . , b_(A+L-1)} are L CRC bits.

S302. the first interleaving sequence π2′ is constituted by sequentiallyextracting all indexes less than A or greater than or equal to K_(max)from the maximum-length interleaving sequence and subtracting K_(max)−Afrom indexes greater than or equal to K_(max) in the extracted indexes

For example, as shown in FIG. 5, if the maximum-length interleavingsequence π2 is {1, 2, 6, 8, 9, 12, 0, 5, 7, 13, 4, 11, 14, 3, 10, 15},L=4, and A=10, a maximum information bit quantity K_(max) correspondingto the maximum-length interleaving sequence is equal to 12, andK_(max)−A=2. All indexes less than 10 or greater than or equal to 12 arefirst sequentially extracted from π2, and an extracted part is {1, 2, 6,8, 9, 12, 0, 5, 7, 13, 4, 14, 3, 15}. Then, 2 is subtracted from indexesgreater than or equal to 12 in the extracted indexes, to constitute thefirst interleaving sequence π2′ {1, 2, 6, 8, 9, 10, 0, 5, 7, 11, 4, 12,3, 13}.

S303. Arrange A information bits in the first bit sequence in descendingorder of information bit indexes, to obtain a third bit sequence.

Specifically, the A information bits in the first bit sequence {b₀, b₁,. . . , b_(A+L-1)} are arranged in descending order of the informationbit indexes, to obtain the third bit sequence {b₀′, b₁′, . . . ,b_(A+L-1)′}. When k=0, 1, . . . , A−1, b_(k)′=b_(A−1-k). When k=A, A+1,. . . , A+L−1, b_(k)′=b_(k).

S304. Perform an interleaving operation on the third bit sequence {b₀′,b₁′, . . . , b_(A+L-1)′} by using the first interleaving sequence π2′,to obtain a second bit sequence.

Specifically, the first bit sequence shown in FIG. 5 is {b₀, b₁, . . . ,b₁₃}. 10 information bits in the first bit sequence {b₀, b₁, . . . ,b₁₃} are arranged in descending order of information bit indexes, toobtain the third bit sequence {b₉, b₈, b₇, b₆, b₅, b₄, b₃, b₂, b₁, b₀,b₁₀, b₁₁, b₁₂, b₁₃}. The second bit sequence obtained after theinterleaving operation is performed on the third bit sequence {b₉, b₈,b₇, b₆, b₅, b₄, b₃, b₂, b₁, b₀, b₁₀, b₁₁, b₁₂, b₁₃} by using the firstinterleaving sequence π2′ {1, 2, 6, 8, 9, 10, 0, 5, 7, 11, 4, 12, 3, 13}is {b₈, b₇, b₃, b₁, b₀, b₁₀, b₉, b₄, b₂, b₁₁, b₅, b₁₂, b₆, b₁₃}.

S305. Perform polar encoding on the second bit sequence.

In this embodiment, as shown in the following Table 2, for aninterleaving sequence in Table 2, different CRC polynomials andcorresponding interleaving sequences for which reverse-order numberingis used are provided for different CRC lengths L and different maximuminformation bit quantities K_(max).

TABLE 2 CRC Interleaving sequence for which reverse-order numbering isK_(max) L polynomial used 200 19 0xA2B79 2, 3, 4, 10, 12, 13, 16, 17,21, 24, 26, 30, 33, 36, 37, 38, 40, 47, 50, 51, 54, 55, 59, 62, 65, 66,68, 69, 70, 71, 72, 74, 86, 87, 89, 90, 92, 94, 95, 96, 99, 105, 106,109, 110, 113, 114, 123, 126, 127, 129, 130, 132, 135, 137, 138, 139,141, 142, 143, 144, 147, 148, 152, 154, 155, 157, 160, 162, 164, 166,168, 173, 175, 176, 177, 179, 180, 181, 185, 186, 188, 189, 192, 193,194, 197, 198, 199, 200, 0, 1, 8, 11, 14, 15, 19, 22, 28, 31, 34, 35,45, 48, 49, 52, 53, 57, 60, 63, 64, 67, 84, 85, 88, 93, 97, 103, 104,107, 108, 111, 112, 121, 124, 125, 128, 133, 136, 140, 145, 146, 150,153, 158, 171, 174, 178, 183, 184, 187, 190, 191, 195, 196, 202, 7, 9,18, 23, 27, 44, 56, 83, 91, 102, 120, 134, 149, 151, 159, 161, 163, 165,170, 172, 182, 203, 5, 20, 29, 39, 43, 73, 77, 78, 81, 98, 100, 101,119, 122, 131, 156, 167, 209, 42, 46, 61, 76, 80, 118, 210, 6, 25, 32,41, 58, 75, 79, 82, 117, 211, 116, 169, 212, 115, 201, 204, 205, 206,207, 208, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197,194, 193, 192, 189, 188, 186, 185, 181, 180, 179, 177, 176, 175, 173,168, 166, 164, 162, 160, 157, 155, 154, 152, 148, 147, 144, 143, 142,141, 139, 138, 137, 135, 132, 130, 129, 127, 126, 123, 114, 113, 110,109, 106, 105, 99, 96, 95, 94, 92, 90, 89, 87, 86, 74, 72, 71, 70, 69,68, 66, 65, 62, 59, 55, 54, 51, 50, 47, 40, 38, 37, 36, 33, 30, 26, 24,21, 17, 16, 13, 12, 10, 4, 3, 2, 200, 196, 195, 191, 190, 187, 184, 183,178, 174, 171, 158, 153, 150, 146, 145, 140, 136, 133, 128, 125, 124,121, 112, 111, 108, 107, 104, 103, 97, 93, 88, 85, 84, 67, 64, 63, 60,57, 53, 52, 49, 48, 45, 35, 34, 31, 28, 22, 19, 15, 14, 11, 8, 1, 0,202, 182, 172, 170, 165, 163, 161, 159, 151, 149, 134, 120, 102, 91, 83,56, 44, 27, 23, 18, 9, 7, 203, 167, 156, 131, 122, 119, 101, 100, 98,81, 78, 77, 73, 43, 39, 29, 20, 5, 209, 118, 80, 76, 61, 46, 42, 210,117, 82, 79, 75, 58, 41, 32, 25, 6, 211, 169, 116, 212, 115, 201, 204,205, 206, 207, 208, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2,8, 10, 11, 14, 15, 19, 22, 24, 28, 31, 34, 35, 36, 38, 45, 48, 49, 52,53, 57, 60, 63, 64, 66, 67, 68, 69, 70, 72, 84, 85, 87, 88, 90, 92, 93,94, 97, 103, 104, 107, 108, 111, 112, 121, 124, 125, 127, 128, 130, 133,135, 136, 137, 139, 140, 141, 142, 145, 146, 150, 152, 153, 155, 158,160, 162, 164, 166, 171, 173, 174, 175, 177, 178, 179, 183, 184, 186,187, 190, 191, 192, 195, 196, 197, 198, 199, 202, 3, 4, 7, 9, 12, 16,17, 18, 23, 26, 27, 40, 44, 50, 54, 55, 56, 74, 83, 91, 95, 99, 102,105, 109, 113, 114, 120, 134, 143, 147, 148, 149, 151, 159, 161, 163,165, 168, 170, 172, 180, 181, 182, 188, 193, 203, 5, 13, 20, 29, 30, 39,42, 47, 51, 58, 59, 62, 65, 73, 81, 82, 89, 96, 98, 100, 101, 106, 110,118, 123, 131, 138, 144, 156, 167, 176, 205, 6, 25, 37, 41, 46, 61, 71,80, 117, 122, 132, 169, 185, 194, 206, 43, 77, 78, 119, 129, 189, 209,21, 32, 75, 76, 79, 157, 211, 33, 116, 154, 212, 86, 115, 126, 200, 201,204, 207, 208, 210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 199,198, 197, 196, 195, 192, 191, 190, 187, 186, 184, 183, 179, 178, 177,175, 174, 173, 171, 166, 164, 162, 160, 158, 155, 153, 152, 150, 146,145, 142, 141, 140, 139, 137, 136, 135, 133, 130, 128, 127, 125, 124,121, 112, 111, 108, 107, 104, 103, 97, 94, 93, 92, 90, 88, 87, 85, 84,72, 70, 69, 68, 67, 66, 64, 63, 60, 57, 53, 52, 49, 48, 45, 38, 36, 35,34, 31, 28, 24, 22, 19, 15, 14, 11, 10, 8, 2, 1, 0, 202, 193, 188, 182,181, 180, 172, 170, 168, 165, 163, 161, 159, 151, 149, 148, 147, 143,134, 120, 114, 113, 109, 105, 102, 99, 95, 91, 83, 74, 56, 55, 54, 50,44, 40, 27, 26, 23, 18, 17, 16, 12, 9, 7, 4, 3, 203, 176, 167, 156, 144,138, 131, 123, 118, 110, 106, 101, 100, 98, 96, 89, 82, 81, 73, 65, 62,59, 58, 51, 47, 42, 39, 30, 29, 20, 13, 5, 205, 194, 185, 169, 132, 122,117, 80, 71, 61, 46, 41, 37, 25, 6, 206, 189, 129, 119, 78, 77, 43, 209,157, 79, 76, 75, 32, 21, 211, 154, 116, 33, 212, 86, 115, 126, 200, 201,204, 207, 208, 210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2,3, 4, 7, 9, 12, 14, 16, 17, 18, 23, 24, 26, 27, 34, 35, 36, 38, 40, 44,48, 50, 52, 54, 55, 56, 63, 67, 70, 72, 74, 83, 84, 90, 91, 93, 94, 95,99, 102, 103, 105, 107, 109, 111, 113, 114, 120, 124, 130, 134, 136,137, 140, 142, 143, 145, 147, 148, 149, 151, 155, 159, 160, 161, 162,163, 164, 165, 166, 168, 170, 172, 174, 175, 178, 179, 180, 181, 182,183, 188, 190, 191, 192, 193, 195, 196, 203, 6, 8, 10, 11, 15, 21, 22,25, 30, 39, 43, 49, 53, 59, 65, 68, 73, 82, 86, 87, 96, 98, 101, 104,108, 112, 119, 126, 127, 132, 133, 138, 146, 150, 152, 157, 158, 167,169, 171, 176, 185, 186, 187, 197, 198, 199, 204, 5, 13, 20, 29, 42, 47,51, 58, 62, 64, 66, 81, 85, 89, 97, 100, 106, 110, 118, 123, 125, 131,139, 141, 144, 156, 184, 205, 19, 28, 37, 41, 46, 57, 61, 71, 80, 88,92, 117, 122, 177, 194, 206, 32, 60, 78, 79, 115, 121, 129, 135, 154,173, 189, 208, 33, 69, 76, 77, 128, 210, 116, 153, 213, 31, 45, 75, 200,201, 202, 207, 209, 211, 212, 214, 215, 216, 217, 218 200 19 0xA2B79196, 195, 193, 192, 191, 190, 188, 183, 182, 181, 180, 179, 178, 175,174, 172, 170, 168, 166, 165, 164, 163, 162, 161, 160, 159, 155, 151,149, 148, 147, 145, 143, 142, 140, 137, 136, 134, 130, 124, 120, 114,113, 111, 109, 107, 105, 103, 102, 99, 95, 94, 93, 91, 90, 84, 83, 74,72, 70, 67, 63, 56, 55, 54, 52, 50, 48, 44, 40, 38, 36, 35, 34, 27, 26,24, 23, 18, 17, 16, 14, 12, 9, 7, 4, 3, 2, 1, 0, 203, 199, 198, 197,187, 186, 185, 176, 171, 169, 167, 158, 157, 152, 150, 146, 138, 133,132, 127, 126, 119, 112, 108, 104, 101, 98, 96, 87, 86, 82, 73, 68, 65,59, 53, 49, 43, 39, 30, 25, 22, 21, 15, 11, 10, 8, 6, 204, 184, 156,144, 141, 139, 131, 125, 123, 118, 110, 106, 100, 97, 89, 85, 81, 66,64, 62, 58, 51, 47, 42, 29, 20, 13, 5, 205, 194, 177, 122, 117, 92, 88,80, 71, 61, 57, 46, 41, 37, 28, 19, 206, 189, 173, 154, 135, 129, 121,115, 79, 78, 60, 32, 208, 128, 77, 76, 69, 33, 210, 153, 116, 213, 31,45, 75, 200, 201, 202, 207, 209, 211, 212, 214, 215, 216, 217, 218 20020 0x191513 0, 1, 2, 4, 6, 10, 11, 13, 14, 15, 18, 19, 20, 21, 23, 30,35, 38, 39, 41, 43, 44, 45, 46, 50, 51, 53, 55, 56, 57, 58, 59, 60, 65,66, 67, 69, 72, 73, 75, 78, 81, 83, 84, 85, 87, 88, 89, 91, 92, 94, 96,98, 99, 103, 104, 105, 106, 109, 110, 111, 114, 116, 118, 119, 121, 126,127, 130, 131, 137, 138, 141, 145, 146, 148, 149, 150, 151, 154, 155,157, 159, 161, 163, 166, 167, 168, 172, 173, 178, 180, 181, 182, 184,188, 189, 193, 196, 197, 200, 3, 5, 9, 12, 17, 22, 29, 34, 37, 40, 42,49, 52, 54, 64, 68, 71, 74, 77, 80, 82, 86, 90, 93, 95, 97, 102, 108,113, 115, 117, 120, 125, 129, 136, 140, 144, 147, 153, 156, 158, 160,162, 165, 171, 177, 179, 183, 187, 192, 195, 199, 201, 8, 16, 28, 33,36, 48, 63, 70, 76, 79, 101, 107, 112, 124, 128, 135, 139, 143, 152,164, 170, 176, 186, 191, 194, 198, 202, 7, 27, 32, 47, 62, 100, 123,134, 142, 169, 175, 185, 190, 203, 26, 31, 61, 122, 133, 174, 204, 25,132, 205, 24, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216,217, 218, 219 200 20 0x191513 197, 196, 193, 189, 188, 184, 182, 181,180, 178, 173, 172, 168, 167, 166, 163, 161, 159, 157, 155, 154, 151,150, 149, 148, 146, 145, 141, 138, 137, 131, 130, 127, 126, 121, 119,118, 116, 114, 111, 110, 109, 106, 105, 104, 103, 99, 98, 96, 94, 92,91, 89, 88, 87, 85, 84, 83, 81, 78, 75, 73, 72, 69, 67, 66, 65, 60, 59,58, 57, 56, 55, 53, 51, 50, 46, 45, 44, 43, 41, 39, 38, 35, 30, 23, 21,20, 19, 18, 15, 14, 13, 11, 10, 6, 4, 2, 1, 0, 200, 199, 195, 192, 187,183, 179, 177, 171, 165, 162, 160, 158, 156, 153, 147, 144, 140, 136,129, 125, 120, 117, 115, 113, 108, 102, 97, 95, 93, 90, 86, 82, 80, 77,74, 71, 68, 64, 54, 52, 49, 42, 40, 37, 34, 29, 22, 17, 12, 9, 5, 3,201, 198, 194, 191, 186, 176, 170, 164, 152, 143, 139, 135, 128, 124,112, 107, 101, 79, 76, 70, 63, 48, 36, 33, 28, 16, 8, 202, 190, 185,175, 169, 142, 134, 123, 100, 62, 47, 32, 27, 7, 203, 174, 133, 122, 61,31, 26, 204, 132, 25, 205, 24, 206, 207, 208, 209, 210, 211, 212, 213,214, 215, 216, 217, 218, 219 200 21 0x2E2A69 2, 4, 9, 11, 15, 17, 18,19, 22, 25, 26, 27, 28, 29, 31, 35, 36, 37, 39, 40, 43, 48, 49, 52, 57,58, 61, 62, 63, 64, 65, 66, 68, 72, 74, 81, 85, 86, 88, 89, 90, 91, 94,96, 98, 102, 103, 105, 110, 111, 112, 116, 120, 121, 123, 125, 127, 130,133, 136, 138, 139, 140, 141, 144, 146, 147, 148, 150, 152, 158, 160,164, 166, 167, 169, 170, 171, 172, 173, 176, 178, 180, 182, 184, 185,187, 189, 190, 191, 193, 194, 198, 200, 1, 3, 8, 10, 14, 16, 21, 24, 30,34, 38, 42, 47, 51, 56, 60, 67, 71, 73, 80, 84, 87, 93, 95, 97, 101,104, 109, 115, 119, 122, 124, 126, 129, 132, 135, 137, 143, 145, 149,151, 157, 159, 163, 165, 168, 175, 177, 179, 181, 183, 186, 188, 192,197, 199, 201, 0, 7, 13, 20, 23, 33, 41, 46, 50, 55, 59, 70, 79, 83, 92,100, 108, 114, 118, 128, 131, 134, 142, 156, 162, 174, 196, 202, 6, 12,32, 45, 54, 69, 78, 82, 99, 107, 113, 117, 155, 161, 195, 203, 5, 44,53, 77, 106, 154, 204, 76, 153, 205, 75, 206, 207, 208, 209, 210, 211,212, 213, 214, 215, 216, 217, 218, 219, 220 200 21 0x2E2A69 198, 194,193, 191, 190, 189, 187, 185, 184, 182, 180, 178, 176, 173, 172, 171,170, 169, 167, 166, 164, 160, 158, 152, 150, 148, 147, 146, 144, 141,140, 139, 138, 136, 133, 130, 127, 125, 123, 121, 120, 116, 112, 111,110, 105, 103, 102, 98, 96, 94, 91, 90, 89, 88, 86, 85, 81, 74, 72, 68,66, 65, 64, 63, 62, 61, 58, 57, 52, 49, 48, 43, 40, 39, 37, 36, 35, 31,29, 28, 27, 26, 25, 22, 19, 18, 17, 15, 11, 9, 4, 2, 200, 199, 197, 192,188, 186, 183, 181, 179, 177, 175, 168, 165, 163, 159, 157, 151, 149,145, 143, 137, 135, 132, 129, 126, 124, 122, 119, 115, 109, 104, 101,97, 95, 93, 87, 84, 80, 73, 71, 67, 60, 56, 51, 47, 42, 38, 34, 30, 24,21, 16, 14, 10, 8, 3, 1, 201, 196, 174, 162, 156, 142, 134, 131, 128,118, 114, 108, 100, 92, 83, 79, 70, 59, 55, 50, 46, 41, 33, 23, 20, 13,7, 0, 202, 195, 161, 155, 117, 113, 107, 99, 82, 78, 69, 54, 45, 32, 12,6, 203, 154, 106, 77, 53, 44, 5, 204, 153, 76, 205, 75, 206, 207, 208,209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220 200 220x552A55 1, 7, 8, 9, 10, 14, 16, 17, 19, 24, 25, 27, 28, 29, 30, 34, 38,40, 47, 49, 50, 51, 52, 57, 58, 61, 63, 65, 67, 68, 69, 70, 74, 77, 78,80, 82, 83, 86, 88, 89, 91, 92, 93, 94, 97, 104, 106, 107, 112, 113,114, 115, 117, 118, 119, 123, 124, 125, 127, 130, 131, 132, 134, 137,138, 139, 141, 142, 143, 147, 148, 149, 150, 151, 154, 155, 158, 159,160, 161, 162, 163, 164, 165, 169, 172, 175, 177, 179, 180, 182, 184,185, 187, 195, 196, 197, 198, 200, 0, 6, 13, 15, 18, 23, 26, 33, 37, 39,46, 48, 56, 60, 62, 64, 66, 73, 76, 79, 81, 85, 87, 90, 96, 103, 105,111, 116, 122, 126, 129, 133, 136, 140, 146, 153, 157, 168, 171, 174,176, 178, 181, 183, 186, 194, 201, 5, 12, 22, 32, 36, 45, 55, 59, 72,75, 84, 95, 102, 110, 121, 128, 135, 145, 152, 156, 167, 170, 173, 193,202, 4, 11, 21, 31, 35, 44, 54, 71, 101, 109, 120, 144, 166, 192, 199,203, 3, 20, 43, 53, 100, 108, 191, 204, 2, 42, 99, 190, 205, 41, 98,189, 206, 188, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217,218, 219, 220, 221 200 22 0x552A55 198, 197, 196, 195, 187, 185, 184,182, 180, 179, 177, 175, 172, 169, 165, 164, 163, 162, 161, 160, 159,158, 155, 154, 151, 150, 149, 148, 147, 143, 142, 141, 139, 138, 137,134, 132, 131, 130, 127, 125, 124, 123, 119, 118, 117, 115, 114, 113,112, 107, 106, 104, 97, 94, 93, 92, 91, 89, 88, 86, 83, 82, 80, 78, 77,74, 70, 69, 68, 67, 65, 63, 61, 58, 57, 52, 51, 50, 49, 47, 40, 38, 34,30, 29, 28, 27, 25, 24, 19, 17, 16, 14, 10, 9, 8, 7, 1, 200, 194, 186,183, 181, 178, 176, 174, 171, 168, 157, 153, 146, 140, 136, 133, 129,126, 122, 116, 111, 105, 103, 96, 90, 87, 85, 81, 79, 76, 73, 66, 64,62, 60, 56, 48, 46, 39, 37, 33, 26, 23, 18, 15, 13, 6, 0, 201, 193, 173,170, 167, 156, 152, 145, 135, 128, 121, 110, 102, 95, 84, 75, 72, 59,55, 45, 36, 32, 22, 12, 5, 202, 199, 192, 166, 144, 120, 109, 101, 71,54, 44, 35, 31, 21, 11, 4, 203, 191, 108, 100, 53, 43, 20, 3, 204, 190,99, 42, 2, 205, 189, 98, 41, 206, 188, 207, 208, 209, 210, 211, 212,213, 214, 215, 216, 217, 218, 219, 220, 221 200 23 0x86F4A1 4, 6, 11,12, 17, 18, 19, 20, 21, 23, 24, 30, 31, 33, 35, 37, 40, 42, 45, 46, 47,50, 51, 54, 55, 57, 58, 59, 60, 62, 64, 65, 66, 75, 76, 78, 80, 83, 84,86, 87, 88, 90, 93, 95, 97, 98, 100, 105, 106, 109, 110, 111, 112, 113,114, 115, 116, 119, 122, 124, 125, 126, 127, 128, 129, 130, 132, 134,135, 138, 139, 140, 142, 144, 146, 148, 149, 150, 152, 153, 154, 157,160, 162, 166, 167, 168, 169, 171, 174, 175, 176, 179, 181, 185, 186,187, 188, 194, 195, 196, 198, 200, 3, 5, 10, 16, 22, 29, 32, 34, 36, 39,41, 44, 49, 53, 56, 61, 63, 74, 77, 79, 82, 85, 89, 92, 94, 96, 99, 104,108, 118, 121, 123, 131, 133, 137, 141, 143, 145, 147, 151, 156, 159,161, 165, 170, 173, 178, 180, 184, 193, 197, 199, 201, 2, 9, 15, 28, 38,43, 48, 52, 73, 81, 91, 103, 107, 117, 120, 136, 155, 158, 164, 172,177, 183, 192, 202, 1, 8, 14, 27, 72, 102, 163, 182, 191, 203, 0, 7, 13,26, 71, 101, 190, 204, 25, 70, 189, 205, 69, 206, 68, 207, 67, 208, 209,210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222 200 230x86F4A1 198, 196, 195, 194, 188, 187, 186, 185, 181, 179, 176, 175,174, 171, 169, 168, 167, 166, 162, 160, 157, 154, 153, 152, 150, 149,148, 146, 144, 142, 140, 139, 138, 135, 134, 132, 130, 129, 128, 127,126, 125, 124, 122, 119, 116, 115, 114, 113, 112, 111, 110, 109, 106,105, 100, 98, 97, 95, 93, 90, 88, 87, 86, 84, 83, 80, 78, 76, 75, 66,65, 64, 62, 60, 59, 58, 57, 55, 54, 51, 50, 47, 46, 45, 42, 40, 37, 35,33, 31, 30, 24, 23, 21, 20, 19, 18, 17, 12, 11, 6, 4, 200, 199, 197,193, 184, 180, 178, 173, 170, 165, 161, 159, 156, 151, 147, 145, 143,141, 137, 133, 131, 123, 121, 118, 108, 104, 99, 96, 94, 92, 89, 85, 82,79, 77, 74, 63, 61, 56, 53, 49, 44, 41, 39, 36, 34, 32, 29, 22, 16, 10,5, 3, 201, 192, 183, 177, 172, 164, 158, 155, 136, 120, 117, 107, 103,91, 81, 73, 52, 48, 43, 38, 28, 15, 9, 2, 202, 191, 182, 163, 102, 72,27, 14, 8, 1, 203, 190, 101, 71, 26, 13, 7, 0, 204, 189, 70, 25, 205,69, 206, 68, 207, 67, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217,218, 219, 220, 221, 222 200 24 0x1D11A9B 0, 1, 5, 7, 10, 12, 13, 16, 17,19, 20, 21, 24, 26, 28, 29, 31, 33, 35, 38, 41, 44, 46, 48, 50, 51, 52,56, 57, 58, 62, 63, 67, 68, 69, 70, 72, 73, 74, 77, 78, 80, 81, 83, 85,86, 88, 89, 90, 94, 97, 105, 108, 111, 113, 114, 115, 119, 120, 125,130, 132, 135, 137, 139, 140, 142, 144, 145, 149, 150, 152, 153, 155,157, 158, 159, 160, 161, 162, 164, 166, 167, 171, 175, 177, 179, 180,183, 186, 187, 188, 191, 193, 194, 196, 197, 199, 200, 4, 6, 9, 11, 15,18, 23, 25, 27, 30, 32, 34, 37, 40, 43, 45, 47, 49, 55, 61, 66, 71, 76,79, 82, 84, 87, 93, 96, 104, 107, 110, 112, 118, 124, 129, 131, 134,136, 138, 141, 143, 148, 151, 154, 156, 163, 165, 170, 174, 176, 178,182, 185, 190, 192, 195, 198, 201, 3, 8, 14, 22, 36, 39, 42, 54, 60, 65,75, 92, 95, 103, 106, 109, 117, 123, 128, 133, 147, 169, 173, 181, 184,189, 202, 2, 53, 59, 64, 91, 102, 116, 122, 127, 146, 168, 172, 203,101, 121, 126, 204, 100, 205, 99, 206, 98, 207, 208, 209, 210, 211, 212,213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223 200 24 0x1D11A9B199, 197, 196, 194, 193, 191, 188, 187, 186, 183, 180, 179, 177, 175,171, 167, 166, 164, 162, 161, 160, 159, 158, 157, 155, 153, 152, 150,149, 145, 144, 142, 140, 139, 137, 135, 132, 130, 125, 120, 119, 115,114, 113, 111, 108, 105, 97, 94, 90, 89, 88, 86, 85, 83, 81, 80, 78, 77,74, 73, 72, 70, 69, 68, 67, 63, 62, 58, 57, 56, 52, 51, 50, 48, 46, 44,41, 38, 35, 33, 31, 29, 28, 26, 24, 21, 20, 19, 17, 16, 13, 12, 10, 7,5, 1, 0, 200, 198, 195, 192, 190, 185, 182, 178, 176, 174, 170, 165,163, 156, 154, 151, 148, 143, 141, 138, 136, 134, 131, 129, 124, 118,112, 110, 107, 104, 96, 93, 87, 84, 82, 79, 76, 71, 66, 61, 55, 49, 47,45, 43, 40, 37, 34, 32, 30, 27, 25, 23, 18, 15, 11, 9, 6, 4, 201, 189,184, 181, 173, 169, 147, 133, 128, 123, 117, 109, 106, 103, 95, 92, 75,65, 60, 54, 42, 39, 36, 22, 14, 8, 3, 202, 172, 168, 146, 127, 122, 116,102, 91, 64, 59, 53, 2, 203, 126, 121, 101, 204, 100, 205, 99, 206, 98,207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,221, 222, 223 1000 11 0x94F 0, 3, 4, 5, 7, 8, 9, 10, 12, 14, 15, 16, 18,19, 20, 21, 22, 23, 24, 25, 27, 31, 32, 33, 37, 38, 40, 41, 42, 43, 44,48, 50, 52, 53, 55, 57, 59, 60, 61, 62, 64, 66, 70, 74, 78, 79, 80, 82,85, 86, 87, 88, 91, 94, 96, 99, 101, 102, 104, 106, 107, 108, 110, 113,114, 120, 121, 122, 123, 125, 126, 127, 128, 129, 131, 137, 139, 140,142, 143, 147, 150, 151, 155, 158, 160, 164, 165, 166, 167, 169, 170,173, 176, 177, 179, 180, 182, 183, 188, 190, 192, 193, 196, 197, 202,203, 205, 208, 211, 212, 215, 216, 217, 221, 222, 223, 225, 226, 229,231, 233, 237, 238, 240, 241, 242, 247, 249, 250, 251, 254, 255, 256,257, 258, 261, 263, 265, 267, 268, 269, 270, 271, 274, 275, 276, 277,278, 279, 280, 281, 284, 291, 292, 297, 302, 303, 305, 307, 313, 318,320, 321, 324, 325, 327, 328, 330, 332, 335, 337, 338, 339, 342, 345,346, 347, 348, 352, 354, 355, 357, 360, 371, 372, 375, 376, 377, 379,380, 381, 382, 384, 386, 387, 388, 390, 391, 392, 393, 394, 395, 396,397, 399, 403, 404, 405, 409, 410, 412, 413, 414, 415, 416, 420, 422,424, 425, 427, 429, 431, 432, 433, 434, 436, 438, 442, 446, 450, 451,452, 454, 457, 458, 459, 460, 463, 466, 468, 471, 473, 474, 476, 478,479, 480, 482, 485, 486, 492, 493, 494, 495, 497, 498, 499, 500, 501,503, 509, 511, 512, 514, 515, 519, 522, 523, 527, 530, 532, 536, 537,538, 539, 541, 542, 545, 548, 549, 551, 552, 554, 555, 560, 562, 564,565, 568, 569, 574, 575, 577, 580, 583, 584, 587, 588, 589, 593, 594,595, 597, 598, 601, 603, 605, 609, 610, 612, 613, 614, 619, 621, 622,623, 626, 627, 628, 629, 630, 633, 635, 637, 639, 640, 641, 642, 643,646, 647, 648, 649, 650, 651, 652, 653, 656, 663, 664, 669, 674, 675,677, 679, 685, 690, 692, 693, 696, 697, 699, 700, 702, 704, 707, 709,710, 711, 714, 717, 718, 719, 720, 724, 726, 727, 729, 732, 743, 744,747, 748, 749, 751, 752, 753, 754, 756, 758, 759, 760, 762, 763, 764,765, 766, 767, 768, 769, 771, 775, 776, 777, 781, 782, 784, 785, 786,787, 788, 792, 794, 796, 797, 799, 801, 803, 804, 805, 806, 808, 810,814, 818, 822, 823, 824, 826, 829, 830, 831, 832, 835, 838, 840, 843,845, 846, 848, 850, 851, 852, 854, 857, 858, 864, 865, 866, 867, 869,870, 871, 872, 873, 875, 881, 883, 884, 886, 887, 891, 894, 895, 899,902, 904, 908, 909, 910, 911, 913, 914, 917, 920, 921, 923, 924, 926,927, 932, 934, 936, 937, 940, 941, 946, 947, 949, 952, 955, 956, 959,960, 961, 965, 966, 967, 969, 970, 973, 975, 977, 981, 982, 984, 985,986, 991, 993, 994, 995, 998, 999, 1000, 2, 6, 11, 13, 17, 26, 30, 36,39, 47, 49, 51, 54, 56, 58, 63, 65, 69, 73, 77, 81, 84, 90, 93, 95, 98,100, 103, 105, 109, 112, 119, 124, 130, 136, 138, 141, 146, 149, 154,157, 159, 163, 168, 172, 175, 178, 181, 187, 189, 191, 195, 201, 204,207, 210, 214, 220, 224, 228, 230, 232, 236, 239, 246, 248, 253, 260,262, 264, 266, 273, 283, 290, 296, 301, 304, 306, 312, 317, 319, 323,326, 329, 331, 334, 336, 341, 344, 351, 353, 356, 359, 370, 374, 378,383, 385, 389, 398, 402, 408, 411, 419, 421, 423, 426, 428, 430, 435,437, 441, 445, 449, 453, 456, 462, 465, 467, 470, 472, 475, 477, 481,484, 491, 496, 502, 508, 510, 513, 518, 521, 526, 529, 531, 535, 540,544, 547, 550, 553, 559, 561, 563, 567, 573, 576, 579, 582, 586, 592,596, 600, 602, 604, 608, 611, 618, 620, 625, 632, 634, 636, 638, 645,655, 662, 668, 673, 676, 678, 684, 689, 691, 695, 698, 701, 703, 706,708, 713, 716, 723, 725, 728, 731, 742, 746, 750, 755, 757, 761, 770,774, 780, 783, 791, 793, 795, 798, 800, 802, 807, 809, 813, 817, 821,825, 828, 834, 837, 839, 842, 844, 847, 849, 853, 856, 863, 868, 874,880, 882, 885, 890, 893, 898, 901, 903, 907, 912, 916, 919, 922, 925,931, 933, 935, 939, 945, 948, 951, 954, 958, 964, 968, 972, 974, 976,980, 983, 990, 992, 997, 1001, 1, 29, 35, 46, 68, 72, 76, 83, 89, 92,97, 111, 118, 135, 145, 148, 153, 156, 162, 171, 174, 186, 194, 200,206, 209, 213, 219, 227, 235, 245, 252, 259, 272, 282, 289, 295, 300,311, 316, 322, 333, 340, 343, 350, 358, 369, 373, 401, 407, 418, 440,444, 448, 455, 461, 464, 469, 483, 490, 507, 517, 520, 525, 528, 534,543, 546, 558, 566, 572, 578, 581, 585, 591, 599, 607, 617, 624, 631,644, 654, 661, 667, 672, 683, 688, 694, 705, 712, 715, 722, 730, 741,745, 773, 779, 790, 812, 816, 820, 827, 833, 836, 841, 855, 862, 879,889, 892, 897, 900, 906, 915, 918, 930, 938, 944, 950, 953, 957, 963,971, 979, 989, 996, 1002, 28, 34, 45, 67, 71, 75, 117, 134, 144, 152,161, 185, 199, 218, 234, 244, 288, 294, 299, 310, 315, 349, 368, 400,406, 417, 439, 443, 447, 489, 506, 516, 524, 533, 557, 571, 590, 606,616, 660, 666, 671, 682, 687, 721, 740, 772, 778, 789, 811, 815, 819,861, 878, 888, 896, 905, 929, 943, 962, 978, 988, 1003, 116, 133, 184,198, 243, 287, 293, 298, 309, 314, 367, 488, 505, 556, 570, 615, 659,665, 670, 681, 686, 739, 860, 877, 928, 942, 987, 1004, 115, 132, 286,308, 366, 487, 504, 658, 680, 738, 859, 876, 1005, 285, 365, 657, 737,1006, 364, 736, 1007, 363, 735, 1008, 362, 734, 1009, 361, 733, 10101000 11 0x94F 999, 998, 995, 994, 993, 991, 986, 985, 984, 982, 981,977, 975, 973, 970, 969, 967, 966, 965, 961, 960, 959, 956, 955, 952,949, 947, 946, 941, 940, 937, 936, 934, 932, 927, 926, 924, 923, 921,920, 917, 914, 913, 911, 910, 909, 908, 904, 902, 899, 895, 894, 891,887, 886, 884, 883, 881, 875, 873, 872, 871, 870, 869, 867, 866, 865,864, 858, 857, 854, 852, 851, 850, 848, 846, 845, 843, 840, 838, 835,832, 831, 830, 829, 826, 824, 823, 822, 818, 814, 810, 808, 806, 805,804, 803, 801, 799, 797, 796, 794, 792, 788, 787, 786, 785, 784, 782,781, 777, 776, 775, 771, 769, 768, 767, 766, 765, 764, 763, 762, 760,759, 758, 756, 754, 753, 752, 751, 749, 748, 747, 744, 743, 732, 729,727, 726, 724, 720, 719, 718, 717, 714, 711, 710, 709, 707, 704, 702,700, 699, 697, 696, 693, 692, 690, 685, 679, 677, 675, 674, 669, 664,663, 656, 653, 652, 651, 650, 649, 648, 647, 646, 643, 642, 641, 640,639, 637, 635, 633, 630, 629, 628, 627, 626, 623, 622, 621, 619, 614,613, 612, 610, 609, 605, 603, 601, 598, 597, 595, 594, 593, 589, 588,587, 584, 583, 580, 577, 575, 574, 569, 568, 565, 564, 562, 560, 555,554, 552, 551, 549, 548, 545, 542, 541, 539, 538, 537, 536, 532, 530,527, 523, 522, 519, 515, 514, 512, 511, 509, 503, 501, 500, 499, 498,497, 495, 494, 493, 492, 486, 485, 482, 480, 479, 478, 476, 474, 473,471, 468, 466, 463, 460, 459, 458, 457, 454, 452, 451, 450, 446, 442,438, 436, 434, 433, 432, 431, 429, 427, 425, 424, 422, 420, 416, 415,414, 413, 412, 410, 409, 405, 404, 403, 399, 397, 396, 395, 394, 393,392, 391, 390, 388, 387, 386, 384, 382, 381, 380, 379, 377, 376, 375,372, 371, 360, 357, 355, 354, 352, 348, 347, 346, 345, 342, 339, 338,337, 335, 332, 330, 328, 327, 325, 324, 321, 320, 318, 313, 307, 305,303, 302, 297, 292, 291, 284, 281, 280, 279, 278, 277, 276, 275, 274,271, 270, 269, 268, 267, 265, 263, 261, 258, 257, 256, 255, 254, 251,250, 249, 247, 242, 241, 240, 238, 237, 233, 231, 229, 226, 225, 223,222, 221, 217, 216, 215, 212, 211, 208, 205, 203, 202, 197, 196, 193,192, 190, 188, 183, 182, 180, 179, 177, 176, 173, 170, 169, 167, 166,165, 164, 160, 158, 155, 151, 150, 147, 143, 142, 140, 139, 137, 131,129, 128, 127, 126, 125, 123, 122, 121, 120, 114, 113, 110, 108, 107,106, 104, 102, 101, 99, 96, 94, 91, 88, 87, 86, 85, 82, 80, 79, 78, 74,70, 66, 64, 62, 61, 60, 59, 57, 55, 53, 52, 50, 48, 44, 43, 42, 41, 40,38, 37, 33, 32, 31, 27, 25, 24, 23, 22, 21, 20, 19, 18, 16, 15, 14, 12,10, 9, 8, 7, 5, 4, 3, 0, 1000, 997, 992, 990, 983, 980, 976, 974, 972,968, 964, 958, 954, 951, 948, 945, 939, 935, 933, 931, 925, 922, 919,916, 912, 907, 903, 901, 898, 893, 890, 885, 882, 880, 874, 868, 863,856, 853, 849, 847, 844, 842, 839, 837, 834, 828, 825, 821, 817, 813,809, 807, 802, 800, 798, 795, 793, 791, 783, 780, 774, 770, 761, 757,755, 750, 746, 742, 731, 728, 725, 723, 716, 713, 708, 706, 703, 701,698, 695, 691, 689, 684, 678, 676, 673, 668, 662, 655, 645, 638, 636,634, 632, 625, 620, 618, 611, 608, 604, 602, 600, 596, 592, 586, 582,579, 576, 573, 567, 563, 561, 559, 553, 550, 547, 544, 540, 535, 531,529, 526, 521, 518, 513, 510, 508, 502, 496, 491, 484, 481, 477, 475,472, 470, 467, 465, 462, 456, 453, 449, 445, 441, 437, 435, 430, 428,426, 423, 421, 419, 411, 408, 402, 398, 389, 385, 383, 378, 374, 370,359, 356, 353, 351, 344, 341, 336, 334, 331, 329, 326, 323, 319, 317,312, 306, 304, 301, 296, 290, 283, 273, 266, 264, 262, 260, 253, 248,246, 239, 236, 232, 230, 228, 224, 220, 214, 210, 207, 204, 201, 195,191, 189, 187, 181, 178, 175, 172, 168, 163, 159, 157, 154, 149, 146,141, 138, 136, 130, 124, 119, 112, 109, 105, 103, 100, 98, 95, 93, 90,84, 81, 77, 73, 69, 65, 63, 58, 56, 54, 51, 49, 47, 39, 36, 30, 26, 17,13, 11, 6, 2, 1001, 996, 989, 979, 971, 963, 957, 953, 950, 944, 938,930, 918, 915, 906, 900, 897, 892, 889, 879, 862, 855, 841, 836, 833,827, 820, 816, 812, 790, 779, 773, 745, 741, 730, 722, 715, 712, 705,694, 688, 683, 672, 667, 661, 654, 644, 631, 624, 617, 607, 599, 591,585, 581, 578, 572, 566, 558, 546, 543, 534, 528, 525, 520, 517, 507,490, 483, 469, 464, 461, 455, 448, 444, 440, 418, 407, 401, 373, 369,358, 350, 343, 340, 333, 322, 316, 311, 300, 295, 289, 282, 272, 259,252, 245, 235, 227, 219, 213, 209, 206, 200, 194, 186, 174, 171, 162,156, 153, 148, 145, 135, 118, 111, 97, 92, 89, 83, 76, 72, 68, 46, 35,29, 1, 1002, 988, 978, 962, 943, 929, 905, 896, 888, 878, 861, 819, 815,811, 789, 778, 772, 740, 721, 687, 682, 671, 666, 660, 616, 606, 590,571, 557, 533, 524, 516, 506, 489, 447, 443, 439, 417, 406, 400, 368,349, 315, 310, 299, 294, 288, 244, 234, 218, 199, 185, 161, 152, 144,134, 117, 75, 71, 67, 45, 34, 28, 1003, 987, 942, 928, 877, 860, 739,686, 681, 670, 665, 659, 615, 570, 556, 505, 488, 367, 314, 309, 298,293, 287, 243, 198, 184, 133, 116, 1004, 876, 859, 738, 680, 658, 504,487, 366, 308, 286, 132, 115, 1005, 737, 657, 365, 285, 1006, 736, 364,1007, 735, 363, 1008, 734, 362, 1009, 733, 361, 1010 22 3 0xD 20, 17,16, 15, 13, 10, 9, 8, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7,23, 4, 24 22 3 0xD 17, 16, 15, 13, 20, 9, 10, 8, 19, 2, 21, 18, 6, 3, 1,14, 12, 22, 11, 0, 5, 7, 23, 4, 24 22 3 0xD 20, 17, 16, 15, 13, 9, 10,8, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24 22 3 0xD20, 17, 16, 15, 9, 10, 8, 13, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0,5, 7, 23, 4, 24

For example, L=19, the polynomial is 0xA2B79, and the interleavingsequence π2={2, 3, 4, 10, 12, 13, 16, 17, 21, 24, 26, 30, 33, 36, 37,38, 40, 47, 50, 51, 54, 55, 59, 62, 65, 66, 68, 69, 70, 71, 72, 74, 86,87, 89, 90, 92, 94, 95, 96, 99, 105, 106, 109, 110, 113, 114, 123, 126,127, 129, 130, 132, 135, 137, 138, 139, 141, 142, 143, 144, 147, 148,152, 154, 155, 157, 160, 162, 164, 166, 168, 173, 175, 176, 177, 179,180, 181, 185, 186, 188, 189, 192, 193, 194, 197, 198, 199, 200, 1, 9,11, 15, 20, 23, 25, 29, 32, 35, 39, 46, 49, 53, 58, 61, 64, 67, 73, 85,88, 91, 93, 98, 104, 108, 112, 122, 125, 128, 131, 134, 136, 140, 146,151, 153, 156, 159, 161, 163, 165, 167, 172, 174, 178, 184, 187, 191,196, 201, 0, 8, 14, 19, 22, 28, 31, 34, 45, 48, 52, 57, 60, 63, 84, 97,103, 107, 111, 121, 124, 133, 145, 150, 158, 171, 183, 190, 195, 202, 7,18, 27, 44, 56, 83, 102, 120, 149, 170, 182, 203, 6, 43, 82, 101, 119,169, 204, 5, 42, 81, 100, 118, 205, 41, 80, 117, 206, 79, 116, 207, 78,115, 208, 77, 209, 76, 210, 75, 211, 212, 213, 214, 215, 216, 217, 218}.For example, if a length A of a current information bit sequence isequal to 64, a bit sequence obtained after CRC encoding is {b₀, b₁, . .. , b₈₂}. A currently required interleaving sequence π2′={2, 3, 4, 10,12, 13, 16, 17, 21, 24, 26, 30, 33, 36, 37, 38, 40, 47, 50, 51, 54, 55,59, 62, 64, 1, 9, 11, 15, 20, 23, 25, 29, 32, 35, 39, 46, 49, 53, 58,61, 65, 0, 8, 14, 19, 22, 28, 31, 34, 45, 48, 52, 57, 60, 63, 66, 7, 18,27, 44, 56, 67, 6, 43, 68, 5, 42, 69, 41, 70, 71, 72, 73, 74, 75, 76,77, 78, 79, 80, 81, 82} is extracted from the interleaving sequence π2based on S302. The sequence {b₀, b₁, . . . , b₈₂} is interleaved basedon S303 and S304, to obtain {c₀, c₁, . . . , c₈₂}={b₆₁, b₆₀, b₅₉, b₅₃,b₅₁, b₅₀, b₄₇, b₄₆, b₄₂, b₃₉, b₃₇, b₃₃, b₃₀, b₂₇, b₂₆, b₂₅, b₂₃, b₁₆,b₁₃, b₁₂, b₉, b₈, b₄, b₁, b₆₄, b₆₂, b₅₄, b₅₂, b₄₈, b₄₃, b₄₀, b₃₈, b₃₄,b₃₁, b₂₈, b₂₄, b₁₇, b₁₄, b₁₀, b₅, b₂, b₆₅, b₆₃, b₅₅, b₄₉, b₄₄, b₄₁, b₃₅,b₃₂, b₂₉, b₁₈, b₁₅, b₁₁, b₆, b₃, b₀, b₆₆, b₅₆, b₄₅, b₃₆, b₁₉, b₇, b₆₇,b₅₇, b₂₀, b₆₈, b₅₈, b₂₁, b₆₉, b₂₂, b₇₀, b₇₁, b₇₂, b₇₃, b₇₄, b₇₅, b₇₆,b₇₇, b₇₈, b₇₉, b₈₀, b₈₁, b₈₂}.

In table 2, when K_(max)=200, L=19, and the CRC polynomial is 0xA2B79,there are six corresponding interleaving sequences for whichreverse-order numbering is used. A better early termination effect isachieved when a first interleaving sequence, a third interleavingsequence, or a fifth interleaving sequence is used for a high code-ratepolar code. A better early termination effect is achieved when a secondinterleaving sequence, a fourth interleaving sequence, or a sixthinterleaving sequence is used for a low code-rate polar code. A betterearly termination effect is achieved when a first interleaving sequenceor a second interleaving sequence is used for polar code SC decoding. Abetter early termination effect is achieved when a third interleavingsequence or a fourth interleaving sequence is used for a polar code witha long code length. A better early termination effect is achieved when afifth interleaving sequence or a sixth interleaving sequence is used fora polar code with a short code length. For example, the long code lengthis a code length greater than 512, and the short code length is a codelength less than 512.

When K_(max)=200, L=20, and the CRC polynomial is 0x191513, there aretwo corresponding interleaving sequences for which reverse-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a high code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a low code-rate polar code.

When K_(max)=200, L=21, and the CRC polynomial is 0x2E2A69, there aretwo corresponding interleaving sequences for which reverse-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a high code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a low code-rate polar code.

When K_(max)=200, L=22, and the CRC polynomial is 0x552A55, there aretwo corresponding interleaving sequences for which reverse-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a high code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a low code-rate polar code.

When K_(max)=200, L=23, and the CRC polynomial is 0x86F4A1, there aretwo corresponding interleaving sequences for which reverse-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a high code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a low code-rate polar code.

When K_(max)=200, L=24, and the CRC polynomial is 0x1D11A9B, there aretwo corresponding interleaving sequences for which reverse-ordernumbering is used. A better early termination effect is achieved when afirst interleaving sequence is used for a high code-rate polar code. Abetter early termination effect is achieved when a second interleavingsequence is used for a low code-rate polar code.

When K_(max)=1000, L=11, and the CRC polynomial is 0x94F, there are twocorresponding interleaving sequences for which reverse-order numberingis used. A better early termination effect is achieved when a firstinterleaving sequence is used for a high code-rate polar code. A betterearly termination effect is achieved when a second interleaving sequenceis used for a low code-rate polar code.

When K_(max)=22, L=3, and the CRC polynomial is 0xD, there are fourcorresponding interleaving sequences for which reverse-order numberingis used. A better early termination effect is achieved when a firstinterleaving sequence is used for a polar code whose code length is 32after encoding. A better early termination effect is achieved when asecond interleaving sequence is used for a polar code whose code lengthis 64 after encoding. A better early termination effect is achieved whena third interleaving sequence is used for a polar code whose code lengthis 128 after encoding. A better early termination effect is achievedwhen a fourth interleaving sequence is used for a polar code whose codelength is 256 after encoding.

FIG. 6 is a schematic flowchart of an encoding method according to thisapplication. In this embodiment, for example, an interleaving sequenceused for an interleaving operation is a maximum-length interleavingsequence, the maximum-length interleaving sequence used for distributedCRC encoding is a sequence π3 for which natural-order numbering is used,a maximum information bit length corresponding to 73 is K_(max), a CRCpolynomial is g, and a CRC bit quantity is L. In other words, a CRClength is L. It is assumed that A to-be-encoded information bits are{a₀, a₁, . . . , a_(A−1)}, and the information bit quantity A≤K_(max).This embodiment is performed by a transmit end (an encoder). As shown inFIG. 6, the method in this embodiment includes the following steps.

S401. Perform CRC encoding on A to-be-encoded information bits, toobtain a first bit sequence {b₀, b₁, . . . , b_(A+L-1)}.

{b₀, b₁, . . . , b_(A−1)} are A information bits, and {b_(A), b_(A+1), .. . , b_(A+L-1)} are L CRC bits.

S402. Extend the first bit sequence {b, b₁, . . . , b_(A+L-1)} to afourth bit sequence {c₀, c₁, . . . , c_(Kmax+L-1))} including K_(max)+Lbits, where values of first K_(max)−A bits in the fourth bit sequenceare set to NULL, and remaining bits sequentially correspond to the bitsin the first bit sequence from a (K_(max)−A+1)^(th) bit.

Specifically, the first bit sequence {b₀, b₁, . . . , b_(A+L-1)} isextended, to obtain the fourth bit sequence {c₀, c₁, . . . ,c_(Kmax+L-1)}. When k=0, 1, . . . , K_(max)−A−1, c_(k)=NULL. Whenk=K_(max)−A, K_(max)−A+1, . . . , K_(max)+L−1, c_(k)=b_((k-(Kmax-A))).

For example, as shown in FIG. 6, the first bit sequence shown in FIG. 6is {b₀, b₁, . . . , b₁₃}, and the obtained fourth bit sequence is {NULL,NULL, b₀, b₁, . . . , b₁₃}.

S403. Perform an interleaving operation on the fourth bit sequence {c₀,c₁, . . . , c_(Kmax+L-1)} by using a maximum-length interleavingsequence π3, to obtain a fifth bit sequence {d₀, d₁, . . . ,d_(Kmax+L-1)}.

For example, as shown in FIG. 6, π3 is {2, 3, 5, 9, 10, 12, 4, 6, 11,13, 0, 7, 14, 1, 8, 15}. The interleaving operation is performed on thefourth bit sequence {NULL, NULL, b₀, b₁, . . . , b₁₃} shown in FIG. 6 byusing π3, to obtain the fifth bit sequence {b₀, b₁, b₃, b₇, b₈, b₁₀, b₂,b₄, b₉, b₁₁, NULL, b₅, b₁₂, NULL, b₆, b₁₃}.

S404. Obtain the second bit sequence {e₀, e₁, . . . , e_(A+L-1))} byremoving the bits whose values are NULL from the fifth bit sequence {d₀,d₁, . . . , d_(Kmax+L-1}.)

For example, as shown in FIG. 6, the bits whose values are NULL areremoved from the fifth bit sequence {b₀, b₁, b₃, b₇, b₈, b₁₀, b₂, b₄,b₉, b₁₁, NULL, b₅, b₁₂, NULL, b₆, b₁₃}, to obtain the second bitsequence e_(n) {b₀, b₁, b₃, b₇, b₈, b₁₀, b₂, b₄, b₉, b₁₁, b₅, b₁₂, b₆,b₁₃}.

S405. Perform polar encoding on the second bit sequence.

In this embodiment, as shown in the foregoing Table 1, for aninterleaving sequence in Table 1, different CRC polynomials andcorresponding interleaving sequences for which natural-order numberingis used are provided for different CRC lengths L and different maximuminformation bit quantities K_(max). For details, refer to Table 1.Different interleaving sequences are applicable to a different scenario.For details, refer to the descriptions of the sequences in Table 1. Thedetails are not described herein again.

For example, L=19, the polynomial is 0xA2B79, and the interleavingsequence π3={0, 1, 2, 5, 6, 7, 10, 11, 13, 14, 14, 19, 20, 22, 23, 24,26, 31, 33, 35, 37, 39, 42, 44, 45, 47, 51, 52, 55, 56, 57, 58, 60, 61,62, 64, 67, 69, 70, 72, 73, 76, 85, 86, 89, 90, 93, 94, 100, 103, 104,105, 107, 109, 110, 112, 113, 125, 127, 128, 129, 130, 131, 133, 134,137, 140, 144, 145, 148, 149, 152, 159, 161, 162, 163, 166, 169, 173,175, 178, 182, 183, 186, 187, 189, 195, 196, 197, 200, 3, 8, 12, 15, 21,25, 27, 32, 34, 36, 38, 40, 43, 46, 48, 53, 59, 63, 65, 68, 71, 74, 77,87, 91, 95, 101, 106, 108, 111, 114, 126, 132, 135, 138, 141, 146, 150,153, 160, 164, 167, 170, 174, 176, 179, 184, 188, 190, 198, 201, 4, 9,16, 28, 41, 49, 54, 66, 75, 78, 88, 92, 96, 102, 115, 136, 139, 142,147, 151, 154, 165, 168, 171, 177, 180, 185, 191, 199, 202, 17, 29, 50,79, 97, 116, 143, 155, 172, 181, 192, 203, 30, 80, 98, 117, 156, 193,204, 81, 99, 118, 157, 194, 205, 82, 119, 158, 206, 83, 120, 207, 84,121, 208, 122, 209, 123, 210, 124, 211, 212, 213, 214, 215, 216, 217,218}. For example, if a length A of a current information bit sequenceis equal to 64, a bit sequence obtained after CRC encoding is {b₀, b₁, .. . , b₈₂}. The sequence {c₀, c₁, . . . , c_(Kmax+L-1)}={NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, b₀, b₁, b₂, b₃, b₄, b₅, b₆, b₇, b₈, b₉, b₁₀, b₁₁, b₁₂, b₁₃,b₁₄, b₁₅, b₁₆, b₁₇, b₁₈, b₁₉, b₂₀, b₂₁, b₂₂, b₂₃, b₂₄, b₂₅, b₂₆, b₂₇,b₂₈, b₂₉, b₃₀, b₃₁, b₃₂, b₃₃, b₃₄, b₃₅, b₃₆, b₃₇, b₃₈, b₃₉, b₄₀, b₄₁,b₄₂, b₄₃, b₄₄, b₄₅, b₄₆, b₄₇, b₄₈, b₄₉, b₅₀, b₅₁, b₅₂, b₅₃, b₅₄, b₅₅,b₅₆, b₅₇, b₅₈, b₅₉, b₆₀, b₆₁, b₆₂, b₆₃, b₆₄, b₆₅, b₆₆, b₆₇, b₆₈, b₆₉,b₇₀, b₇₁, b₇₂, b₇₃, b₇₄, b₇₅, b₇₆, b₇₇, b₇₈, b₇₉, b₈₀, b₈₁, b₈₂} isfirst obtained based on S402. The {c₀, c₁, . . . , c_(Kmax+L-1)} isinterleaved based on S403 and the interleaving sequence π3, to obtain{d₀, d₁, . . . , d_(Kmax+L-1)}={NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, b₁,b₄, b₈, b₉, b₁₂, b₁₃, b₁₆, b₂₃, b₂₅, b₂₆, b₂₇, b₃₀, b₃₃, b₃₇, b₃₉, b₄₂,b₄₆, b₄₇, b₅₀, b₅₁, b₅₃, b₅₉, b₆₀, b₆₁, b₆₄, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, b₂, b₅, b₁₀, b₁₄, b₁₇, b₂₄, b₂₈,b₃₁, b₃₄, b₃₈, b₄₀, b₄₃, b₄₈, b₅₂, b₅₄, b₆₂, b₆₅, NULL, NULL, NULL,NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,b₀, b₃, b₆, b₁₁, b₁₅, b₁₈, b₂₉, b₃₂, b₃₅, b₄₁, b₄₄, b₄₉, b₅₅, b₆₃, b₆₆,NULL, NULL, NULL, NULL, NULL, NULL, b₇, b₁₉, b₃₆, b₄₅, b₅₆, b₆₇, NULL,NULL, NULL, NULL, b₂₀₀, b₅₇, b₆₈, NULL, NULL, NULL, b₂₁, b₅₈, b₆₉, NULL,NULL, b₂₂, b₇₀, NULL, NULL, b₇₁, NULL, NULL, b₇₂, NULL, b₇₃, NULL, b₇₄,NULL, b₇₅, b₇₆, b₇₇, b₇₈, b₇₉, b₈₀, b₈₁, b₈₂}. NULL bits are removedfrom {d₀, d₁, . . . , d_(Kmax+L-1)} based on S404, to obtain thesequence {e₀, e₁, . . . , e_(A+L-1)}={b₁, b₄, b₈, b₉, b₁₂, b₁₃, b₁₆,b₂₃, b₂₅, b₂₆, b₂₇, b₃₀, b₃₃, b₃₇, b₃₉, b₄₂, b₄₆, b₄₇, b₅₀, b₅₁, b₅₃,b₅₉, b₆₀, b₆₁, b₆₄, b₂, b₅, b₁₀, b₁₄, b₁₇, b₂₄, b₂₈, b₃₁, b₃₄, b₃₈, b₄₀,b₄₃, b₄₈, b₅₂, b₅₄, b₆₂, b₆₅, b₀, b₃, b₆, b₁₁, b₁₅, b₁₈, b₂₉, b₃₂, b₃₅,b₄₁, b₄₄, b₄₉, b₅₅, b₆₃, b₆₆, b₇, b₁₉, b₃₆, b₄₅, b₅₆, b₆₇, b₂₀, b₅₇,b₆₈, b₂₁, b₅₈, b₆₉, b₂₂, b₇₀, b₇₁, b₇₂, b₇₃, b₇₄, b₇₅, b₇₆, b₇₇, b₇₈,b₇₉, b₈₀, b₈₁, b₈₂}.

It should be noted that a receive end (a decoder side) needs to performa de-interleaving operation after receiving to-be-decoded informationbits. A process in which the receive end (decoder) obtains aninterleaving sequence during de-interleaving is consistent with aprocess in which the transmit end (an encoder side) obtains aninterleaving sequence during interleaving. For details, refer to thedescriptions of the encoder. The details are not described herein.

In this application, the transmit end may be divided into functionmodules based on the foregoing method examples. For example, eachfunction module may be obtained through division for a correspondingfunction, or two or more functions may be integrated into one processingmodule. The integrated module may be implemented in a form of hardware,or may be implemented in a form of a software function module. It shouldbe noted that module division in the embodiments of this application ismerely an example, is merely logical function division, and may be otherdivision during actual implementation.

FIG. 7 is a schematic structural diagram of an embodiment of an encodingapparatus according to this application. As shown in FIG. 7, theapparatus in this embodiment may include a first encoding module 11, aninterleaving module 12, and a second encoding module 13. The firstencoding module 11 is configured to perform cyclic redundancy check CRCencoding on A to-be-encoded information bits, to obtain a first bitsequence. The first bit sequence includes L CRC bits and A informationbits, and L and A are positive integers. The interleaving module 12 isconfigured to perform an interleaving operation on the first bitsequence, to obtain a second bit sequence. A first interleaving sequenceused for the interleaving operation is obtained based on asystem-supported maximum-length interleaving sequence and a preset rule,and a length of the first interleaving sequence is equal to A+L.Alternatively, a second interleaving sequence used for the interleavingoperation is the maximum-length interleaving sequence, a length of thesecond interleaving sequence is equal to K_(max)+L, and K_(max) is amaximum information bit quantity corresponding to the maximum-lengthinterleaving sequence. The second encoding module 13 is configured toperform polar encoding on the second bit sequence.

Optionally, the preset rule is: the first interleaving sequence issequentially constituted by extracting all indexes greater than or equalto K_(max)−A from the maximum-length interleaving sequence andsubtracting K_(max)−A from each of all the extracted indexes. Theinterleaving module 12 is configured to perform the interleavingoperation on the first bit sequence by using the first interleavingsequence, to obtain the second bit sequence. The maximum-lengthinterleaving sequence is any sequence in the foregoing Table 1.

Optionally, the preset rule is: the first interleaving sequence isconstituted by sequentially extracting all indexes less than A orgreater than or equal to K_(max) from the maximum-length interleavingsequence and subtracting K_(max)−A from indexes greater than or equal toK_(max) in the extracted indexes. The interleaving module 12 isconfigured to: arrange the A information bits in the first bit sequencein descending order of information bit indexes, to obtain a third bitsequence; and perform the interleaving operation on the third bitsequence by using the first interleaving sequence, to obtain the secondbit sequence. The maximum-length interleaving sequence is any sequencein the foregoing Table 2.

Optionally, when the second interleaving sequence used for theinterleaving operation is the maximum-length interleaving sequence, theinterleaving module 12 is configured to: extend the first bit sequenceto a fourth bit sequence including K_(max)+L bits, where values of firstK_(max)−A bits in the fourth bit sequence are set to NULL, and remainingbits sequentially correspond to the bits in the first bit sequence froma (K_(max)−A+1)^(th) bit; perform the interleaving operation on thefourth bit sequence by using the maximum-length interleaving sequence,to obtain a fifth bit sequence; and obtain the second bit sequence byremoving the bits whose values are NULL from the fifth bit sequence. Themaximum-length interleaving sequence is any sequence in the foregoingTable 1.

The apparatus in this embodiment may be configured to perform thetechnical solutions in the method embodiment shown in FIG. 3. Animplementation principle and technical effects of the apparatus aresimilar to those of the method embodiment. Details are not describedherein again.

FIG. 8 is a schematic diagram of an encoding entity apparatus accordingto this application. The apparatus 1100 includes a memory 1101 and aprocessor 1102.

The memory 1101 is configured to store a program instruction. The memorymay be a flash memory (flash memory).

The processor 1102 is configured to: invoke and execute the programinstruction in the memory, to perform the steps in the encoding methodshown in FIG. 3. For details, refer to the related descriptions in theforegoing method embodiment.

Optionally, the memory 1101 may be independent, or may be arranged asshown in FIG. 9. FIG. 9 is a schematic diagram of an encoding entityapparatus according to this application. The memory 1101 is integratedinto the processor 1102.

The apparatus may be configured to perform the steps and/or proceduresthat correspond to the transmit end in the foregoing method embodiment.

This application further provides a computer system, including areadable storage medium and a computer program. The computer program isconfigured to perform the encoding method provided in the foregoingimplementations.

This application further provides a program product. The program productincludes a computer program, and the computer program is stored in areadable storage medium. At least one processor of an encoding apparatusmay read the computer program from the readable storage medium, and theat least one processor executes the computer program, so that theencoding apparatus performs the encoding method provided in theforegoing implementations.

A person of ordinary skill in the art may understand that all or some ofthe foregoing embodiments may be implemented by using software,hardware, firmware, or any combination thereof. When the embodiments areimplemented by using software, all or some of the embodiments may beimplemented in a form of a computer program product. The computerprogram product includes one or more computer instructions. When thecomputer program instructions are loaded and executed on a computer, allor some of the procedures or functions according to the embodiments ofthe present invention are generated. The computer may be ageneral-purpose computer, a dedicated computer, a computer network, oranother programmable apparatus. The computer instructions may be storedin a computer readable storage medium or may be transmitted from acomputer readable storage medium to another computer readable storagemedium. For example, the computer instructions may be transmitted from awebsite, computer, server, or data center to another website, computer,server, or data center in a wired (for example, a coaxial cable, anoptical fiber, or a digital subscriber line (DSL)) or wireless (forexample, infrared, radio, or microwave) manner. The computer readablestorage medium may be any usable medium accessible to a computer, or maybe a data storage device, such as a server or a data center, integratingone or more usable media. The usable medium may be a magnetic medium(for example, a floppy disk, a hard disk, or a magnetic tape), anoptical medium (for example, DVD), a semiconductor medium (for example,a solid state disk (SSD)), or the like.

What is claimed is:
 1. An encoding method, comprising: performing cyclicredundancy check (CRC) encoding on A to-be-encoded information bits, toobtain a first bit sequence, wherein the first bit sequence comprises LCRC bits and the A to-be-encoded information bits, and L and A arepositive integers; performing an interleaving operation on the first bitsequence, to obtain a second bit sequence, wherein a first interleavingsequence used for the interleaving operation is obtained based on asystem-supported maximum-length interleaving sequence and a preset rule,and a length of the first interleaving sequence is equal to A+L; or asecond interleaving sequence used for the interleaving operation is themaximum-length interleaving sequence, a length of the secondinterleaving sequence is equal to K_(max)+L, and K_(max) is a maximuminformation bit quantity corresponding to the maximum-lengthinterleaving sequence; and performing polar encoding on the second bitsequence.
 2. The method according to claim 1, wherein the preset ruleis: the first interleaving sequence is constituted by extracting allindexes greater than or equal to K_(max)−A from the maximum-lengthinterleaving sequence and subtracting K_(max)−A from each of all theextracted indexes; and the performing an interleaving operation on thefirst bit sequence comprises: performing the interleaving operation onthe first bit sequence by using the first interleaving sequence, toobtain the second bit sequence.
 3. The method according to claim 1,wherein the preset rule is: the first interleaving sequence isconstituted by extracting all indexes less than A or greater than orequal to K_(max) from the maximum-length interleaving sequence andsubtracting K_(max)−A from indexes greater than or equal to K_(max) inthe extracted indexes; and the performing an interleaving operation onthe first bit sequence comprises: obtain a third bit sequence byarranging the A information bits in the first bit sequence in descendingorder of information bit indexes; and performing the interleavingoperation on the third bit sequence by using the first interleavingsequence, to obtain the second bit sequence.
 4. The method according toclaim 1, wherein when the second interleaving sequence used for theinterleaving operation is the maximum-length interleaving sequence, theperforming an interleaving operation on the first bit sequencecomprises: extending the first bit sequence to a fourth bit sequencecomprising K_(max)+L bits, wherein values of first K_(max)−A bits in thefourth bit sequence are set to NULL, and remaining bits sequentiallycorrespond to the bits in the first bit sequence from a(K_(max)−A+1)^(th) bit; performing the interleaving operation on thefourth bit sequence by using the maximum-length interleaving sequence,to obtain a fifth bit sequence; and obtaining the second bit sequence byremoving the bits whose values are NULL from the fifth bit sequence. 5.The method according to claim 1, wherein the maximum-length interleavingsequence is any sequence in the following table: CRC Interleavingsequence for which natural-order numbering is K_(max) L polynomial used200 19 0xA2B79 0, 1, 2, 5, 6, 7, 10, 11, 13, 14, 18, 19, 20, 22, 23, 24,26, 31, 33, 35, 37, 39, 42, 44, 45, 47, 51, 52, 55, 56, 57, 58, 60, 61,62, 64, 67, 69, 70, 72, 73, 76, 85, 86, 89, 90, 93, 94, 100, 103, 104,105, 107, 109, 110, 112, 113, 125, 127, 128, 129, 130, 131, 133, 134,137, 140, 144, 145, 148, 149, 152, 159, 161, 162, 163, 166, 169, 173,175, 178, 182, 183, 186, 187, 189, 195, 196, 197, 200, 3, 4, 8, 9, 12,15, 16, 21, 25, 28, 41, 46, 49, 53, 54, 59, 63, 66, 71, 74, 75, 78, 87,88, 91, 92, 95, 96, 102, 106, 111, 114, 115, 132, 135, 136, 139, 142,146, 147, 150, 151, 154, 164, 165, 168, 171, 177, 180, 184, 185, 188,191, 198, 199, 202, 17, 27, 29, 34, 36, 38, 40, 48, 50, 65, 79, 97, 108,116, 143, 155, 172, 176, 181, 190, 192, 203, 32, 43, 68, 77, 80, 98, 99,101, 118, 121, 122, 126, 156, 160, 170, 179, 194, 209, 81, 119, 123,138, 153, 157, 210, 82, 117, 120, 124, 141, 158, 167, 174, 193, 211, 30,83, 212, 84, 201, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218200 19 0xA2B79 197, 196, 195, 189, 187, 186, 183, 182, 178, 175, 173,169, 166, 163, 162, 161, 159, 152, 149, 148, 145, 144, 140, 137, 134,133, 131, 130, 129, 128, 127, 125, 113, 112, 110, 109, 107, 105, 104,103, 100, 94, 93, 90, 89, 86, 85, 76, 73, 72, 70, 69, 67, 64, 62, 61,60, 58, 57, 56, 55, 52, 51, 47, 45, 44, 42, 39, 37, 35, 33, 31, 26, 24,23, 22, 20, 19, 18, 14, 13, 11, 10, 7, 6, 5, 2, 1, 0, 200, 199, 198,191, 188, 185, 184, 180, 177, 171, 168, 165, 164, 154, 151, 150, 147,146, 142, 139, 136, 135, 132, 115, 114, 111, 106, 102, 96, 95, 92, 91,88, 87, 78, 75, 74, 71, 66, 63, 59, 54, 53, 49, 46, 41, 28, 25, 21, 16,15, 12, 9, 8, 4, 3, 202, 192, 190, 181, 176, 172, 155, 143, 116, 108,97, 79, 65, 50, 48, 40, 38, 36, 34, 29, 27, 17, 203, 194, 179, 170, 160,156, 126, 122, 121, 118, 101, 99, 98, 80, 77, 68, 43, 32, 209, 157, 153,138, 123, 119, 81, 210, 193, 174, 167, 158, 141, 124, 120, 117, 82, 211,83, 30, 212, 84, 201, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217,218 200 19 0xA2B79 0, 1, 2, 3, 4, 7, 8, 9, 12, 13, 15, 16, 20, 21, 22,24, 25, 26, 28, 33, 35, 37, 39, 41, 44, 46, 47, 49, 53, 54, 57, 58, 59,60, 62, 63, 64, 66, 69, 71, 72, 74, 75, 78, 87, 88, 91, 92, 95, 96, 102,105, 106, 107, 109, 111, 112, 114, 115, 127, 129, 130, 131, 132, 133,135, 136, 139, 142, 146, 147, 150, 151, 154, 161, 163, 164, 165, 168,171, 175, 177, 180, 184, 185, 188, 189, 191, 197, 198, 199, 202, 6, 11,17, 18, 19, 27, 29, 31, 34, 36, 38, 40, 48, 50, 51, 52, 56, 65, 79, 85,86, 90, 94, 97, 100, 104, 108, 116, 125, 143, 144, 145, 149, 155, 159,172, 173, 176, 181, 182, 183, 187, 190, 192, 195, 196, 203, 23, 32, 43,55, 61, 68, 76, 81, 89, 93, 98, 99, 101, 103, 110, 117, 118, 126, 134,137, 140, 141, 148, 152, 157, 160, 169, 170, 179, 186, 194, 205, 5, 14,30, 67, 77, 82, 119, 128, 138, 153, 158, 162, 174, 193, 206, 10, 70, 80,121, 122, 156, 209, 42, 120, 123, 124, 167, 178, 211, 45, 83, 166, 212,73, 84, 113, 200, 201, 204, 207, 208, 210, 213, 214, 215, 216, 217, 218200 19 0xA2B79 199, 198, 197, 191, 189, 188, 185, 184, 180, 177, 175,171, 168, 165, 164, 163, 161, 154, 151, 150, 147, 146, 142, 139, 136,135, 133, 132, 131, 130, 129, 127, 115, 114, 112, 111, 109, 107, 106,105, 102, 96, 95, 92, 91, 88, 87, 78, 75, 74, 72, 71, 69, 66, 64, 63,62, 60, 59, 58, 57, 54, 53, 49, 47, 46, 44, 41, 39, 37, 35, 33, 28, 26,25, 24, 22, 21, 20, 16, 15, 13, 12, 9, 8, 7, 4, 3, 2, 1, 0, 202, 196,195, 192, 190, 187, 183, 182, 181, 176, 173, 172, 159, 155, 149, 145,144, 143, 125, 116, 108, 104, 100, 97, 94, 90, 86, 85, 79, 65, 56, 52,51, 50, 48, 40, 38, 36, 34, 31, 29, 27, 19, 18, 17, 11, 6, 203, 194,186, 179, 170, 169, 160, 157, 152, 148, 141, 140, 137, 134, 126, 118,117, 110, 103, 101, 99, 98, 93, 89, 81, 76, 68, 61, 55, 43, 32, 23, 205,193, 174, 162, 158, 153, 138, 128, 119, 82, 77, 67, 30, 14, 5, 206, 156,122, 121, 80, 70, 10, 209, 178, 167, 124, 123, 120, 42, 211, 166, 83,45, 212, 73, 84, 113, 200, 201, 204, 207, 208, 210, 213, 214, 215, 216,217, 218 200 19 0xA2B79 3, 4, 6, 7, 8, 9, 11, 16, 17, 18, 19, 20, 21,24, 25, 27, 29, 31, 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458, 460,461, 462, 463, 467, 469, 472, 476, 477, 480, 484, 485, 487, 488, 490,496, 498, 499, 500, 501, 502, 504, 505, 506, 507, 513, 514, 517, 519,520, 521, 523, 525, 526, 528, 531, 533, 536, 539, 540, 541, 542, 545,547, 548, 549, 553, 557, 561, 563, 565, 566, 567, 568, 570, 572, 574,575, 577, 579, 583, 584, 585, 586, 587, 589, 590, 594, 595, 596, 600,602, 603, 604, 605, 606, 607, 608, 609, 611, 612, 613, 615, 617, 618,619, 620, 622, 623, 624, 627, 628, 639, 642, 644, 645, 647, 651, 652,653, 654, 657, 660, 661, 662, 664, 667, 669, 671, 672, 674, 675, 678,679, 681, 686, 692, 694, 696, 697, 702, 707, 708, 715, 718, 719, 720,721, 722, 723, 724, 725, 728, 729, 730, 731, 732, 734, 736, 738, 741,742, 743, 744, 745, 748, 749, 750, 752, 757, 758, 759, 761, 762, 766,768, 770, 773, 774, 776, 777, 778, 782, 783, 784, 787, 788, 791, 794,796, 797, 802, 803, 806, 807, 809, 811, 816, 817, 819, 820, 822, 823,826, 829, 830, 832, 833, 834, 835, 839, 841, 844, 848, 849, 852, 856,857, 859, 860, 862, 868, 870, 871, 872, 873, 874, 876, 877, 878, 879,885, 886, 889, 891, 892, 893, 895, 897, 898, 900, 903, 905, 908, 911,912, 913, 914, 917, 919, 920, 921, 925, 929, 933, 935, 937, 938, 939,940, 942, 944, 946, 947, 949, 951, 955, 956, 957, 958, 959, 961, 962,966, 967, 968, 972, 974, 975, 976, 977, 978, 979, 980, 981, 983, 984,985, 987, 989, 990, 991, 992, 994, 995, 996, 999, 1000, 2, 7, 9, 16, 19,23, 25, 27, 31, 35, 41, 45, 48, 51, 54, 60, 64, 66, 68, 74, 77, 80, 83,87, 92, 96, 98, 101, 106, 109, 114, 117, 119, 125, 131, 136, 143, 146,150, 152, 155, 157, 160, 162, 165, 171, 174, 178, 182, 186, 190, 192,197, 199, 201, 204, 206, 208, 216, 219, 225, 229, 238, 242, 244, 249,253, 257, 268, 271, 274, 276, 283, 286, 291, 293, 296, 298, 301, 304,308, 310, 315, 321, 323, 326, 331, 337, 344, 354, 361, 363, 365, 367,374, 379, 381, 388, 391, 395, 397, 399, 403, 407, 413, 417, 420, 423,426, 432, 436, 438, 440, 446, 449, 452, 455, 459, 464, 468, 470, 473,478, 481, 486, 489, 491, 497, 503, 508, 515, 518, 522, 524, 527, 529,532, 534, 537, 543, 546, 550, 554, 558, 562, 564, 569, 571, 573, 576,578, 580, 588, 591, 597, 601, 610, 614, 616, 621, 625, 629, 640, 643,646, 648, 655, 658, 663, 665, 668, 670, 673, 676, 680, 682, 687, 693,695, 698, 703, 709, 716, 726, 733, 735, 737, 739, 746, 751, 753, 760,763, 767, 769, 771, 775, 779, 785, 789, 792, 795, 798, 804, 808, 810,812, 818, 821, 824, 827, 831, 836, 840, 842, 845, 850, 853, 858, 861,863, 869, 875, 880, 887, 890, 894, 896, 899, 901, 904, 906, 909, 915,918, 922, 926, 930, 934, 936, 941, 943, 945, 948, 950, 952, 960, 963,969, 973, 982, 986, 988, 993, 997, 1001, 3, 10, 20, 28, 36, 42, 46, 49,55, 61, 69, 81, 84, 93, 99, 102, 107, 110, 120, 137, 144, 158, 163, 166,172, 179, 183, 187, 209, 220, 226, 254, 258, 269, 277, 284, 287, 294,305, 311, 316, 327, 332, 338, 345, 355, 368, 375, 382, 392, 400, 408,414, 418, 421, 427, 433, 441, 453, 456, 465, 471, 474, 479, 482, 492,509, 516, 530, 535, 538, 544, 551, 555, 559, 581, 592, 598, 626, 630,641, 649, 656, 659, 666, 677, 683, 688, 699, 704, 710, 717, 727, 740,747, 754, 764, 772, 780, 786, 790, 793, 799, 805, 813, 825, 828, 837,843, 846, 851, 854, 864, 881, 888, 902, 907, 910, 916, 923, 927, 931,953, 964, 970, 998, 1002, 11, 21, 37, 56, 70, 94, 103, 111, 121, 138,180, 184, 188, 210, 221, 227, 259, 278, 312, 317, 328, 333, 339, 383,393, 409, 428, 442, 466, 475, 483, 493, 510, 552, 556, 560, 582, 593,599, 631, 650, 684, 689, 700, 705, 711, 755, 765, 781, 800, 814, 838,847, 855, 865, 882, 924, 928, 932, 954, 965, 971, 1003, 12, 57, 71, 122,139, 260, 313, 318, 329, 334, 340, 384, 429, 443, 494, 511, 632, 685,690, 701, 706, 712, 756, 801, 815, 866, 883, 1004, 123, 140, 261, 319,341, 495, 512, 633, 691, 713, 867, 884, 1005, 262, 342, 634, 714, 1006,263, 635, 1007, 264, 636, 1008, 265, 637, 1009, 266, 638, 1010 1000 110x94F 999, 996, 995, 994, 992, 991, 990, 989, 987, 985, 984, 983, 981,980, 979, 978, 977, 976, 975, 974, 972, 968, 967, 966, 962, 961, 959,958, 957, 956, 955, 951, 949, 947, 946, 944, 942, 940, 939, 938, 937,935, 933, 929, 925, 921, 920, 919, 917, 914, 913, 912, 911, 908, 905,903, 900, 898, 897, 895, 893, 892, 891, 889, 886, 885, 879, 878, 877,876, 874, 873, 872, 871, 870, 868, 862, 860, 859, 857, 856, 852, 849,848, 844, 841, 839, 835, 834, 833, 832, 830, 829, 826, 823, 822, 820,819, 817, 816, 811, 809, 807, 806, 803, 802, 797, 796, 794, 791, 788,787, 784, 783, 782, 778, 777, 776, 774, 773, 770, 768, 766, 762, 761,759, 758, 757, 752, 750, 749, 748, 745, 744, 743, 742, 741, 738, 736,734, 732, 731, 730, 729, 728, 725, 724, 723, 722, 721, 720, 719, 718,715, 708, 707, 702, 697, 696, 694, 692, 686, 681, 679, 678, 675, 674,672, 671, 669, 667, 664, 662, 661, 660, 657, 654, 653, 652, 651, 647,645, 644, 642, 639, 628, 627, 624, 623, 622, 620, 619, 618, 617, 615,613, 612, 611, 609, 608, 607, 606, 605, 604, 603, 602, 600, 596, 595,594, 590, 589, 587, 586, 585, 584, 583, 579, 577, 575, 574, 572, 570,568, 567, 566, 565, 563, 561, 557, 553, 549, 548, 547, 545, 542, 541,540, 539, 536, 533, 531, 528, 526, 525, 523, 521, 520, 519, 517, 514,513, 507, 506, 505, 504, 502, 501, 500, 499, 498, 496, 490, 488, 487,485, 484, 480, 477, 476, 472, 469, 467, 463, 462, 461, 460, 458, 457,454, 451, 450, 448, 447, 445, 444, 439, 437, 435, 434, 431, 430, 425,424, 422, 419, 416, 415, 412, 411, 410, 406, 405, 404, 402, 401, 398,396, 394, 390, 389, 387, 386, 385, 380, 378, 377, 376, 373, 372, 371,370, 369, 366, 364, 362, 360, 359, 358, 357, 356, 353, 352, 351, 350,349, 348, 347, 346, 343, 336, 335, 330, 325, 324, 322, 320, 314, 309,307, 306, 303, 302, 300, 299, 297, 295, 292, 290, 289, 288, 285, 282,281, 280, 279, 275, 273, 272, 270, 267, 256, 255, 252, 251, 250, 248,247, 246, 245, 243, 241, 240, 239, 237, 236, 235, 234, 233, 232, 231,230, 228, 224, 223, 222, 218, 217, 215, 214, 213, 212, 211, 207, 205,203, 202, 200, 198, 196, 195, 194, 193, 191, 189, 185, 181, 177, 176,175, 173, 170, 169, 168, 167, 164, 161, 159, 156, 154, 153, 151, 149,148, 147, 145, 142, 141, 135, 134, 133, 132, 130, 129, 128, 127, 126,124, 118, 116, 115, 113, 112, 108, 105, 104, 100, 97, 95, 91, 90, 89,88, 86, 85, 82, 79, 78, 76, 75, 73, 72, 67, 65, 63, 62, 59, 58, 53, 52,50, 47, 44, 43, 40, 39, 38, 34, 33, 32, 30, 29, 26, 24, 22, 18, 17, 15,14, 13, 8, 6, 5, 4, 1, 0, 1000, 997, 993, 988, 986, 982, 973, 969, 963,960, 952, 950, 948, 945, 943, 941, 936, 934, 930, 926, 922, 918, 915,909, 906, 904, 901, 899, 896, 894, 890, 887, 880, 875, 869, 863, 861,858, 853, 850, 845, 842, 840, 836, 831, 827, 824, 821, 818, 812, 810,808, 804, 798, 795, 792, 789, 785, 779, 775, 771, 769, 767, 763, 760,753, 751, 746, 739, 737, 735, 733, 726, 716, 709, 703, 698, 695, 693,687, 682, 680, 676, 673, 670, 668, 665, 663, 658, 655, 648, 646, 643,640, 629, 625, 621, 616, 614, 610, 601, 597, 591, 588, 580, 578, 576,573, 571, 569, 564, 562, 558, 554, 550, 546, 543, 537, 534, 532, 529,527, 524, 522, 518, 515, 508, 503, 497, 491, 489, 486, 481, 478, 473,470, 468, 464, 459, 455, 452, 449, 446, 440, 438, 436, 432, 426, 423,420, 417, 413, 407, 403, 399, 397, 395, 391, 388, 381, 379, 374, 367,365, 363, 361, 354, 344, 337, 331, 326, 323, 321, 315, 310, 308, 304,301, 298, 296, 293, 291, 286, 283, 276, 274, 271, 268, 257, 253, 249,244, 242, 238, 229, 225, 219, 216, 208, 206, 204, 201, 199, 197, 192,190, 186, 182, 178, 174, 171, 165, 162, 160, 157, 155, 152, 150, 146,143, 136, 131, 125, 119, 117, 114, 109, 106, 101, 98, 96, 92, 87, 83,80, 77, 74, 68, 66, 64, 60, 54, 51, 48, 45, 41, 35, 31, 27, 25, 23, 19,16, 9, 7, 2, 1001, 998, 970, 964, 953, 931, 927, 923, 916, 910, 907,902, 888, 881, 864, 854, 851, 846, 843, 837, 828, 825, 813, 805, 799,793, 790, 786, 780, 772, 764, 754, 747, 740, 727, 717, 710, 704, 699,688, 683, 677, 666, 659, 656, 649, 641, 630, 626, 598, 592, 581, 559,555, 551, 544, 538, 535, 530, 516, 509, 492, 482, 479, 474, 471, 465,456, 453, 441, 433, 427, 421, 418, 414, 408, 400, 392, 382, 375, 368,355, 345, 338, 332, 327, 316, 311, 305, 294, 287, 284, 277, 269, 258,254, 226, 220, 209, 187, 183, 179, 172, 166, 163, 158, 144, 137, 120,110, 107, 102, 99, 93, 84, 81, 69, 61, 55, 49, 46, 42, 36, 28, 20, 10,3, 1002, 971, 965, 954, 932, 928, 924, 882, 865, 855, 847, 838, 814,800, 781, 765, 755, 711, 705, 700, 689, 684, 650, 631, 599, 593, 582,560, 556, 552, 510, 493, 483, 475, 466, 442, 428, 409, 393, 383, 339,333, 328, 317, 312, 278, 259, 227, 221, 210, 188, 184, 180, 138, 121,111, 103, 94, 70, 56, 37, 21, 11, 1003, 883, 866, 815, 801, 756, 712,706, 701, 690, 685, 632, 511, 494, 443, 429, 384, 340, 334, 329, 318,313, 260, 139, 122, 71, 57, 12, 1004, 884, 867, 713, 691, 633, 512, 495,341, 319, 261, 140, 123, 1005, 714, 634, 342, 262, 1006, 635, 263, 1007,636, 264, 1008, 637, 265, 1009, 638, 266, 1010 22 3 0xD 1, 4, 5, 6, 8,11, 12, 13, 0, 19, 2, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17,24 22 3 0xD 4, 5, 6, 8, 1, 12, 11, 13, 2, 19, 0, 3, 15, 18, 20, 7, 9,22, 10, 21, 16, 14, 23, 17, 24 22 3 0xD 1, 4, 5, 6, 8, 12, 11, 13, 0,19, 2, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24 22 3 0xD 1,4, 5, 6, 12, 11, 13, 8, 0, 19, 2, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16,14, 23, 17, 24


6. The method according to claim 1, wherein the maximum-lengthinterleaving sequence is any sequence in the following table: CRCInterleaving sequence for which reverse-order numbering is K_(max) Lpolynomial used 200 19 0xA2B79 2, 3, 4, 10, 12, 13, 16, 17, 21, 24, 26,30, 33, 36, 37, 38, 40, 47, 50, 51, 54, 55, 59, 62, 65, 66, 68, 69, 70,71, 72, 74, 86, 87, 89, 90, 92, 94, 95, 96, 99, 105, 106, 109, 110, 113,114, 123, 126, 127, 129, 130, 132, 135, 137, 138, 139, 141, 142, 143,144, 147, 148, 152, 154, 155, 157, 160, 162, 164, 166, 168, 173, 175,176, 177, 179, 180, 181, 185, 186, 188, 189, 192, 193, 194, 197, 198,199, 200, 0, 1, 8, 11, 14, 15, 19, 22, 28, 31, 34, 35, 45, 48, 49, 52,53, 57, 60, 63, 64, 67, 84, 85, 88, 93, 97, 103, 104, 107, 108, 111,112, 121, 124, 125, 128, 133, 136, 140, 145, 146, 150, 153, 158, 171,174, 178, 183, 184, 187, 190, 191, 195, 196, 202, 7, 9, 18, 23, 27, 44,56, 83, 91, 102, 120, 134, 149, 151, 159, 161, 163, 165, 170, 172, 182,203, 5, 20, 29, 39, 43, 73, 77, 78, 81, 98, 100, 101, 119, 122, 131,156, 167, 209, 42, 46, 61, 76, 80, 118, 210, 6, 25, 32, 41, 58, 75, 79,82, 117, 211, 116, 169, 212, 115, 201, 204, 205, 206, 207, 208, 213,214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197, 194, 193, 192,189, 188, 186, 185, 181, 180, 179, 177, 176, 175, 173, 168, 166, 164,162, 160, 157, 155, 154, 152, 148, 147, 144, 143, 142, 141, 139, 138,137, 135, 132, 130, 129, 127, 126, 123, 114, 113, 110, 109, 106, 105,99, 96, 95, 94, 92, 90, 89, 87, 86, 74, 72, 71, 70, 69, 68, 66, 65, 62,59, 55, 54, 51, 50, 47, 40, 38, 37, 36, 33, 30, 26, 24, 21, 17, 16, 13,12, 10, 4, 3, 2, 200, 196, 195, 191, 190, 187, 184, 183, 178, 174, 171,158, 153, 150, 146, 145, 140, 136, 133, 128, 125, 124, 121, 112, 111,108, 107, 104, 103, 97, 93, 88, 85, 84, 67, 64, 63, 60, 57, 53, 52, 49,48, 45, 35, 34, 31, 28, 22, 19, 15, 14, 11, 8, 1, 0, 202, 182, 172, 170,165, 163, 161, 159, 151, 149, 134, 120, 102, 91, 83, 56, 44, 27, 23, 18,9, 7, 203, 167, 156, 131, 122, 119, 101, 100, 98, 81, 78, 77, 73, 43,39, 29, 20, 5, 209, 118, 80, 76, 61, 46, 42, 210, 117, 82, 79, 75, 58,41, 32, 25, 6, 211, 169, 116, 212, 115, 201, 204, 205, 206, 207, 208,213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2, 8, 10, 11, 14, 15,19, 22, 24, 28, 31, 34, 35, 36, 38, 45, 48, 49, 52, 53, 57, 60, 63, 64,66, 67, 68, 69, 70, 72, 84, 85, 87, 88, 90, 92, 93, 94, 97, 103, 104,107, 108, 111, 112, 121, 124, 125, 127, 128, 130, 133, 135, 136, 137,139, 140, 141, 142, 145, 146, 150, 152, 153, 155, 158, 160, 162, 164,166, 171, 173, 174, 175, 177, 178, 179, 183, 184, 186, 187, 190, 191,192, 195, 196, 197, 198, 199, 202, 3, 4, 7, 9, 12, 16, 17, 18, 23, 26,27, 40, 44, 50, 54, 55, 56, 74, 83, 91, 95, 99, 102, 105, 109, 113, 114,120, 134, 143, 147, 148, 149, 151, 159, 161, 163, 165, 168, 170, 172,180, 181, 182, 188, 193, 203, 5, 13, 20, 29, 30, 39, 42, 47, 51, 58, 59,62, 65, 73, 81, 82, 89, 96, 98, 100, 101, 106, 110, 118, 123, 131, 138,144, 156, 167, 176, 205, 6, 25, 37, 41, 46, 61, 71, 80, 117, 122, 132,169, 185, 194, 206, 43, 77, 78, 119, 129, 189, 209, 21, 32, 75, 76, 79,157, 211, 33, 116, 154, 212, 86, 115, 126, 200, 201, 204, 207, 208, 210,213, 214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197, 196, 195,192, 191, 190, 187, 186, 184, 183, 179, 178, 177, 175, 174, 173, 171,166, 164, 162, 160, 158, 155, 153, 152, 150, 146, 145, 142, 141, 140,139, 137, 136, 135, 133, 130, 128, 127, 125, 124, 121, 112, 111, 108,107, 104, 103, 97, 94, 93, 92, 90, 88, 87, 85, 84, 72, 70, 69, 68, 67,66, 64, 63, 60, 57, 53, 52, 49, 48, 45, 38, 36, 35, 34, 31, 28, 24, 22,19, 15, 14, 11, 10, 8, 2, 1, 0, 202, 193, 188, 182, 181, 180, 172, 170,168, 165, 163, 161, 159, 151, 149, 148, 147, 143, 134, 120, 114, 113,109, 105, 102, 99, 95, 91, 83, 74, 56, 55, 54, 50, 44, 40, 27, 26, 23,18, 17, 16, 12, 9, 7, 4, 3, 203, 176, 167, 156, 144, 138, 131, 123, 118,110, 106, 101, 100, 98, 96, 89, 82, 81, 73, 65, 62, 59, 58, 51, 47, 42,39, 30, 29, 20, 13, 5, 205, 194, 185, 169, 132, 122, 117, 80, 71, 61,46, 41, 37, 25, 6, 206, 189, 129, 119, 78, 77, 43, 209, 157, 79, 76, 75,32, 21, 211, 154, 116, 33, 212, 86, 115, 126, 200, 201, 204, 207, 208,210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2, 3, 4, 7, 9,12, 14, 16, 17, 18, 23, 24, 26, 27, 34, 35, 36, 38, 40, 44, 48, 50, 52,54, 55, 56, 63, 67, 70, 72, 74, 83, 84, 90, 91, 93, 94, 95, 99, 102,103, 105, 107, 109, 111, 113, 114, 120, 124, 130, 134, 136, 137, 140,142, 143, 145, 147, 148, 149, 151, 155, 159, 160, 161, 162, 163, 164,165, 166, 168, 170, 172, 174, 175, 178, 179, 180, 181, 182, 183, 188,190, 191, 192, 193, 195, 196, 203, 6, 8, 10, 11, 15, 21, 22, 25, 30, 39,43, 49, 53, 59, 65, 68, 73, 82, 86, 87, 96, 98, 101, 104, 108, 112, 119,126, 127, 132, 133, 138, 146, 150, 152, 157, 158, 167, 169, 171, 176,185, 186, 187, 197, 198, 199, 204, 5, 13, 20, 29, 42, 47, 51, 58, 62,64, 66, 81, 85, 89, 97, 100, 106, 110, 118, 123, 125, 131, 139, 141,144, 156, 184, 205, 19, 28, 37, 41, 46, 57, 61, 71, 80, 88, 92, 117,122, 177, 194, 206, 32, 60, 78, 79, 115, 121, 129, 135, 154, 173, 189,208, 33, 69, 76, 77, 128, 210, 116, 153, 213, 31, 45, 75, 200, 201, 202,207, 209, 211, 212, 214, 215, 216, 217, 218 200 19 0xA2B79 196, 195,193, 192, 191, 190, 188, 183, 182, 181, 180, 179, 178, 175, 174, 172,170, 168, 166, 165, 164, 163, 162, 161, 160, 159, 155, 151, 149, 148,147, 145, 143, 142, 140, 137, 136, 134, 130, 124, 120, 114, 113, 111,109, 107, 105, 103, 102, 99, 95, 94, 93, 91, 90, 84, 83, 74, 72, 70, 67,63, 56, 55, 54, 52, 50, 48, 44, 40, 38, 36, 35, 34, 27, 26, 24, 23, 18,17, 16, 14, 12, 9, 7, 4, 3, 2, 1, 0, 203, 199, 198, 197, 187, 186, 185,176, 171, 169, 167, 158, 157, 152, 150, 146, 138, 133, 132, 127, 126,119, 112, 108, 104, 101, 98, 96, 87, 86, 82, 73, 68, 65, 59, 53, 49, 43,39, 30, 25, 22, 21, 15, 11, 10, 8, 6, 204, 184, 156, 144, 141, 139, 131,125, 123, 118, 110, 106, 100, 97, 89, 85, 81, 66, 64, 62, 58, 51, 47,42, 29, 20, 13, 5, 205, 194, 177, 122, 117, 92, 88, 80, 71, 61, 57, 46,41, 37, 28, 19, 206, 189, 173, 154, 135, 129, 121, 115, 79, 78, 60, 32,208, 128, 77, 76, 69, 33, 210, 153, 116, 213, 31, 45, 75, 200, 201, 202,207, 209, 211, 212, 214, 215, 216, 217, 218 200 20 0x191513 0, 1, 2, 4,6, 10, 11, 13, 14, 15, 18, 19, 20, 21, 23, 30, 35, 38, 39, 41, 43, 44,45, 46, 50, 51, 53, 55, 56, 57, 58, 59, 60, 65, 66, 67, 69, 72, 73, 75,78, 81, 83, 84, 85, 87, 88, 89, 91, 92, 94, 96, 98, 99, 103, 104, 105,106, 109, 110, 111, 114, 116, 118, 119, 121, 126, 127, 130, 131, 137,138, 141, 145, 146, 148, 149, 150, 151, 154, 155, 157, 159, 161, 163,166, 167, 168, 172, 173, 178, 180, 181, 182, 184, 188, 189, 193, 196,197, 200, 3, 5, 9, 12, 17, 22, 29, 34, 37, 40, 42, 49, 52, 54, 64, 68,71, 74, 77, 80, 82, 86, 90, 93, 95, 97, 102, 108, 113, 115, 117, 120,125, 129, 136, 140, 144, 147, 153, 156, 158, 160, 162, 165, 171, 177,179, 183, 187, 192, 195, 199, 201, 8, 16, 28, 33, 36, 48, 63, 70, 76,79, 101, 107, 112, 124, 128, 135, 139, 143, 152, 164, 170, 176, 186,191, 194, 198, 202, 7, 27, 32, 47, 62, 100, 123, 134, 142, 169, 175,185, 190, 203, 26, 31, 61, 122, 133, 174, 204, 25, 132, 205, 24, 206,207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 200 200x191513 197, 196, 193, 189, 188, 184, 182, 181, 180, 178, 173, 172,168, 167, 166, 163, 161, 159, 157, 155, 154, 151, 150, 149, 148, 146,145, 141, 138, 137, 131, 130, 127, 126, 121, 119, 118, 116, 114, 111,110, 109, 106, 105, 104, 103, 99, 98, 96, 94, 92, 91, 89, 88, 87, 85,84, 83, 81, 78, 75, 73, 72, 69, 67, 66, 65, 60, 59, 58, 57, 56, 55, 53,51, 50, 46, 45, 44, 43, 41, 39, 38, 35, 30, 23, 21, 20, 19, 18, 15, 14,13, 11, 10, 6, 4, 2, 1, 0, 200, 199, 195, 192, 187, 183, 179, 177, 171,165, 162, 160, 158, 156, 153, 147, 144, 140, 136, 129, 125, 120, 117,115, 113, 108, 102, 97, 95, 93, 90, 86, 82, 80, 77, 74, 71, 68, 64, 54,52, 49, 42, 40, 37, 34, 29, 22, 17, 12, 9, 5, 3, 201, 198, 194, 191,186, 176, 170, 164, 152, 143, 139, 135, 128, 124, 112, 107, 101, 79, 76,70, 63, 48, 36, 33, 28, 16, 8, 202, 190, 185, 175, 169, 142, 134, 123,100, 62, 47, 32, 27, 7, 203, 174, 133, 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363, 735, 1008, 362, 734, 1009, 361, 733, 1010 1000 11 0x94F999, 998, 995, 994, 993, 991, 986, 985, 984, 982, 981, 977, 975, 973,970, 969, 967, 966, 965, 961, 960, 959, 956, 955, 952, 949, 947, 946,941, 940, 937, 936, 934, 932, 927, 926, 924, 923, 921, 920, 917, 914,913, 911, 910, 909, 908, 904, 902, 899, 895, 894, 891, 887, 886, 884,883, 881, 875, 873, 872, 871, 870, 869, 867, 866, 865, 864, 858, 857,854, 852, 851, 850, 848, 846, 845, 843, 840, 838, 835, 832, 831, 830,829, 826, 824, 823, 822, 818, 814, 810, 808, 806, 805, 804, 803, 801,799, 797, 796, 794, 792, 788, 787, 786, 785, 784, 782, 781, 777, 776,775, 771, 769, 768, 767, 766, 765, 764, 763, 762, 760, 759, 758, 756,754, 753, 752, 751, 749, 748, 747, 744, 743, 732, 729, 727, 726, 724,720, 719, 718, 717, 714, 711, 710, 709, 707, 704, 702, 700, 699, 697,696, 693, 692, 690, 685, 679, 677, 675, 674, 669, 664, 663, 656, 653,652, 651, 650, 649, 648, 647, 646, 643, 642, 641, 640, 639, 637, 635,633, 630, 629, 628, 627, 626, 623, 622, 621, 619, 614, 613, 612, 610,609, 605, 603, 601, 598, 597, 595, 594, 593, 589, 588, 587, 584, 583,580, 577, 575, 574, 569, 568, 565, 564, 562, 560, 555, 554, 552, 551,549, 548, 545, 542, 541, 539, 538, 537, 536, 532, 530, 527, 523, 522,519, 515, 514, 512, 511, 509, 503, 501, 500, 499, 498, 497, 495, 494,493, 492, 486, 485, 482, 480, 479, 478, 476, 474, 473, 471, 468, 466,463, 460, 459, 458, 457, 454, 452, 451, 450, 446, 442, 438, 436, 434,433, 432, 431, 429, 427, 425, 424, 422, 420, 416, 415, 414, 413, 412,410, 409, 405, 404, 403, 399, 397, 396, 395, 394, 393, 392, 391, 390,388, 387, 386, 384, 382, 381, 380, 379, 377, 376, 375, 372, 371, 360,357, 355, 354, 352, 348, 347, 346, 345, 342, 339, 338, 337, 335, 332,330, 328, 327, 325, 324, 321, 320, 318, 313, 307, 305, 303, 302, 297,292, 291, 284, 281, 280, 279, 278, 277, 276, 275, 274, 271, 270, 269,268, 267, 265, 263, 261, 258, 257, 256, 255, 254, 251, 250, 249, 247,242, 241, 240, 238, 237, 233, 231, 229, 226, 225, 223, 222, 221, 217,216, 215, 212, 211, 208, 205, 203, 202, 197, 196, 193, 192, 190, 188,183, 182, 180, 179, 177, 176, 173, 170, 169, 167, 166, 165, 164, 160,158, 155, 151, 150, 147, 143, 142, 140, 139, 137, 131, 129, 128, 127,126, 125, 123, 122, 121, 120, 114, 113, 110, 108, 107, 106, 104, 102,101, 99, 96, 94, 91, 88, 87, 86, 85, 82, 80, 79, 78, 74, 70, 66, 64, 62,61, 60, 59, 57, 55, 53, 52, 50, 48, 44, 43, 42, 41, 40, 38, 37, 33, 32,31, 27, 25, 24, 23, 22, 21, 20, 19, 18, 16, 15, 14, 12, 10, 9, 8, 7, 5,4, 3, 0, 1000, 997, 992, 990, 983, 980, 976, 974, 972, 968, 964, 958,954, 951, 948, 945, 939, 935, 933, 931, 925, 922, 919, 916, 912, 907,903, 901, 898, 893, 890, 885, 882, 880, 874, 868, 863, 856, 853, 849,847, 844, 842, 839, 837, 834, 828, 825, 821, 817, 813, 809, 807, 802,800, 798, 795, 793, 791, 783, 780, 774, 770, 761, 757, 755, 750, 746,742, 731, 728, 725, 723, 716, 713, 708, 706, 703, 701, 698, 695, 691,689, 684, 678, 676, 673, 668, 662, 655, 645, 638, 636, 634, 632, 625,620, 618, 611, 608, 604, 602, 600, 596, 592, 586, 582, 579, 576, 573,567, 563, 561, 559, 553, 550, 547, 544, 540, 535, 531, 529, 526, 521,518, 513, 510, 508, 502, 496, 491, 484, 481, 477, 475, 472, 470, 467,465, 462, 456, 453, 449, 445, 441, 437, 435, 430, 428, 426, 423, 421,419, 411, 408, 402, 398, 389, 385, 383, 378, 374, 370, 359, 356, 353,351, 344, 341, 336, 334, 331, 329, 326, 323, 319, 317, 312, 306, 304,301, 296, 290, 283, 273, 266, 264, 262, 260, 253, 248, 246, 239, 236,232, 230, 228, 224, 220, 214, 210, 207, 204, 201, 195, 191, 189, 187,181, 178, 175, 172, 168, 163, 159, 157, 154, 149, 146, 141, 138, 136,130, 124, 119, 112, 109, 105, 103, 100, 98, 95, 93, 90, 84, 81, 77, 73,69, 65, 63, 58, 56, 54, 51, 49, 47, 39, 36, 30, 26, 17, 13, 11, 6, 2,1001, 996, 989, 979, 971, 963, 957, 953, 950, 944, 938, 930, 918, 915,906, 900, 897, 892, 889, 879, 862, 855, 841, 836, 833, 827, 820, 816,812, 790, 779, 773, 745, 741, 730, 722, 715, 712, 705, 694, 688, 683,672, 667, 661, 654, 644, 631, 624, 617, 607, 599, 591, 585, 581, 578,572, 566, 558, 546, 543, 534, 528, 525, 520, 517, 507, 490, 483, 469,464, 461, 455, 448, 444, 440, 418, 407, 401, 373, 369, 358, 350, 343,340, 333, 322, 316, 311, 300, 295, 289, 282, 272, 259, 252, 245, 235,227, 219, 213, 209, 206, 200, 194, 186, 174, 171, 162, 156, 153, 148,145, 135, 118, 111, 97, 92, 89, 83, 76, 72, 68, 46, 35, 29, 1, 1002,988, 978, 962, 943, 929, 905, 896, 888, 878, 861, 819, 815, 811, 789,778, 772, 740, 721, 687, 682, 671, 666, 660, 616, 606, 590, 571, 557,533, 524, 516, 506, 489, 447, 443, 439, 417, 406, 400, 368, 349, 315,310, 299, 294, 288, 244, 234, 218, 199, 185, 161, 152, 144, 134, 117,75, 71, 67, 45, 34, 28, 1003, 987, 942, 928, 877, 860, 739, 686, 681,670, 665, 659, 615, 570, 556, 505, 488, 367, 314, 309, 298, 293, 287,243, 198, 184, 133, 116, 1004, 876, 859, 738, 680, 658, 504, 487, 366,308, 286, 132, 115, 1005, 737, 657, 365, 285, 1006, 736, 364, 1007, 735,363, 1008, 734, 362, 1009, 733, 361, 1010 22 3 0xD 20, 17, 16, 15, 13,10, 9, 8, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24 223 0xD 17, 16, 15, 13, 20, 9, 10, 8, 19, 2, 21, 18, 6, 3, 1, 14, 12, 22,11, 0, 5, 7, 23, 4, 24 22 3 0xD 20, 17, 16, 15, 13, 9, 10, 8, 21, 2, 19,18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24 22 3 0xD 20, 17, 16, 15,9, 10, 8, 13, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24


7. An encoding apparatus, comprising: a memory configured to store aprogram instruction; and a processor configured to perform cyclicredundancy check (CRC) encoding on A to-be-encoded information bits, toobtain a first bit sequence, wherein the first bit sequence comprises LCRC bits and A information bits, and L and A are positive integers,perform an interleaving operation on the first bit sequence, to obtain asecond bit sequence wherein a first interleaving sequence used for theinterleaving operation is obtained based on a system-supportedmaximum-length interleaving sequence and a preset rule, and a length ofthe first interleaving sequence is equal to A+L; or a secondinterleaving sequence used for the interleaving operation is themaximum-length interleaving sequence, a length of the secondinterleaving sequence is equal to K_(max)+L, and K_(max) is a maximuminformation bit quantity corresponding to the maximum-lengthinterleaving sequence, and perform polar encoding on the second bitsequence.
 8. The apparatus according to claim 7, wherein the preset ruleis: the first interleaving sequence is constituted by extracting allindexes greater than or equal to K_(max)−A from the maximum-lengthinterleaving sequence and subtracting K_(max)−A from each of all theextracted indexes; and the processor is configured to: perform theinterleaving operation on the first bit sequence by using the firstinterleaving sequence, to obtain the second bit sequence.
 9. Theapparatus according to claim 7, wherein the preset rule is: the firstinterleaving sequence is constituted by extracting all indexes less thanA or greater than or equal to K_(max) from the maximum-lengthinterleaving sequence and subtracting K_(max)−A from indexes greaterthan or equal to K_(max) in the extracted indexes; and the processor isconfigured to: arrange the A information bits in the first bit sequencein descending order of information bit indexes, to obtain a third bitsequence; and perform the interleaving operation on the third bitsequence by using the first interleaving sequence, to obtain the secondbit sequence.
 10. The apparatus according to claim 7, wherein when thesecond interleaving sequence used for the interleaving operation is themaximum-length interleaving sequence, the processor is configured to:extend the first bit sequence to a fourth bit sequence comprisingK_(max)+L bits, wherein values of first K_(max)−A bits in the fourth bitsequence are set to NULL, and remaining bits sequentially correspond tothe bits in the first bit sequence from a (K_(max)−A+1)^(th) bit;perform the interleaving operation on the fourth bit sequence by usingthe maximum-length interleaving sequence, to obtain a fifth bitsequence; and obtain the second bit sequence by removing the bits whosevalues are NULL from the fifth bit sequence.
 11. The apparatus accordingto claim 7, wherein the maximum-length interleaving sequence is anysequence in the following table: CRC Interleaving sequence for whichnatural-order numbering is K_(max) L polynomial used 200 19 0xA2B79 0,1, 2, 5, 6, 7, 10, 11, 13, 14, 18, 19, 20, 22, 23, 24, 26, 31, 33, 35,37, 39, 42, 44, 45, 47, 51, 52, 55, 56, 57, 58, 60, 61, 62, 64, 67, 69,70, 72, 73, 76, 85, 86, 89, 90, 93, 94, 100, 103, 104, 105, 107, 109,110, 112, 113, 125, 127, 128, 129, 130, 131, 133, 134, 137, 140, 144,145, 148, 149, 152, 159, 161, 162, 163, 166, 169, 173, 175, 178, 182,183, 186, 187, 189, 195, 196, 197, 200, 3, 4, 8, 9, 12, 15, 16, 21, 25,28, 41, 46, 49, 53, 54, 59, 63, 66, 71, 74, 75, 78, 87, 88, 91, 92, 95,96, 102, 106, 111, 114, 115, 132, 135, 136, 139, 142, 146, 147, 150,151, 154, 164, 165, 168, 171, 177, 180, 184, 185, 188, 191, 198, 199,202, 17, 27, 29, 34, 36, 38, 40, 48, 50, 65, 79, 97, 108, 116, 143, 155,172, 176, 181, 190, 192, 203, 32, 43, 68, 77, 80, 98, 99, 101, 118, 121,122, 126, 156, 160, 170, 179, 194, 209, 81, 119, 123, 138, 153, 157,210, 82, 117, 120, 124, 141, 158, 167, 174, 193, 211, 30, 83, 212, 84,201, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218 200 190xA2B79 197, 196, 195, 189, 187, 186, 183, 182, 178, 175, 173, 169, 166,163, 162, 161, 159, 152, 149, 148, 145, 144, 140, 137, 134, 133, 131,130, 129, 128, 127, 125, 113, 112, 110, 109, 107, 105, 104, 103, 100,94, 93, 90, 89, 86, 85, 76, 73, 72, 70, 69, 67, 64, 62, 61, 60, 58, 57,56, 55, 52, 51, 47, 45, 44, 42, 39, 37, 35, 33, 31, 26, 24, 23, 22, 20,19, 18, 14, 13, 11, 10, 7, 6, 5, 2, 1, 0, 200, 199, 198, 191, 188, 185,184, 180, 177, 171, 168, 165, 164, 154, 151, 150, 147, 146, 142, 139,136, 135, 132, 115, 114, 111, 106, 102, 96, 95, 92, 91, 88, 87, 78, 75,74, 71, 66, 63, 59, 54, 53, 49, 46, 41, 28, 25, 21, 16, 15, 12, 9, 8, 4,3, 202, 192, 190, 181, 176, 172, 155, 143, 116, 108, 97, 79, 65, 50, 48,40, 38, 36, 34, 29, 27, 17, 203, 194, 179, 170, 160, 156, 126, 122, 121,118, 101, 99, 98, 80, 77, 68, 43, 32, 209, 157, 153, 138, 123, 119, 81,210, 193, 174, 167, 158, 141, 124, 120, 117, 82, 211, 83, 30, 212, 84,201, 204, 205, 206, 207, 208, 213, 214, 215, 216, 217, 218 200 190xA2B79 0, 1, 2, 3, 4, 7, 8, 9, 12, 13, 15, 16, 20, 21, 22, 24, 25, 26,28, 33, 35, 37, 39, 41, 44, 46, 47, 49, 53, 54, 57, 58, 59, 60, 62, 63,64, 66, 69, 71, 72, 74, 75, 78, 87, 88, 91, 92, 95, 96, 102, 105, 106,107, 109, 111, 112, 114, 115, 127, 129, 130, 131, 132, 133, 135, 136,139, 142, 146, 147, 150, 151, 154, 161, 163, 164, 165, 168, 171, 175,177, 180, 184, 185, 188, 189, 191, 197, 198, 199, 202, 6, 11, 17, 18,19, 27, 29, 31, 34, 36, 38, 40, 48, 50, 51, 52, 56, 65, 79, 85, 86, 90,94, 97, 100, 104, 108, 116, 125, 143, 144, 145, 149, 155, 159, 172, 173,176, 181, 182, 183, 187, 190, 192, 195, 196, 203, 23, 32, 43, 55, 61,68, 76, 81, 89, 93, 98, 99, 101, 103, 110, 117, 118, 126, 134, 137, 140,141, 148, 152, 157, 160, 169, 170, 179, 186, 194, 205, 5, 14, 30, 67,77, 82, 119, 128, 138, 153, 158, 162, 174, 193, 206, 10, 70, 80, 121,122, 156, 209, 42, 120, 123, 124, 167, 178, 211, 45, 83, 166, 212, 73,84, 113, 200, 201, 204, 207, 208, 210, 213, 214, 215, 216, 217, 218 20019 0xA2B79 199, 198, 197, 191, 189, 188, 185, 184, 180, 177, 175, 171,168, 165, 164, 163, 161, 154, 151, 150, 147, 146, 142, 139, 136, 135,133, 132, 131, 130, 129, 127, 115, 114, 112, 111, 109, 107, 106, 105,102, 96, 95, 92, 91, 88, 87, 78, 75, 74, 72, 71, 69, 66, 64, 63, 62, 60,59, 58, 57, 54, 53, 49, 47, 46, 44, 41, 39, 37, 35, 33, 28, 26, 25, 24,22, 21, 20, 16, 15, 13, 12, 9, 8, 7, 4, 3, 2, 1, 0, 202, 196, 195, 192,190, 187, 183, 182, 181, 176, 173, 172, 159, 155, 149, 145, 144, 143,125, 116, 108, 104, 100, 97, 94, 90, 86, 85, 79, 65, 56, 52, 51, 50, 48,40, 38, 36, 34, 31, 29, 27, 19, 18, 17, 11, 6, 203, 194, 186, 179, 170,169, 160, 157, 152, 148, 141, 140, 137, 134, 126, 118, 117, 110, 103,101, 99, 98, 93, 89, 81, 76, 68, 61, 55, 43, 32, 23, 205, 193, 174, 162,158, 153, 138, 128, 119, 82, 77, 67, 30, 14, 5, 206, 156, 122, 121, 80,70, 10, 209, 178, 167, 124, 123, 120, 42, 211, 166, 83, 45, 212, 73, 84,113, 200, 201, 204, 207, 208, 210, 213, 214, 215, 216, 217, 218 200 190xA2B79 3, 4, 6, 7, 8, 9, 11, 16, 17, 18, 19, 20, 21, 24, 25, 27, 29,31, 33, 34, 35, 36, 37, 38, 39, 40, 44, 48, 50, 51, 52, 54, 56, 57, 59,62, 63, 65, 69, 75, 79, 85, 86, 88, 90, 92, 94, 96, 97, 100, 104, 105,106, 108, 109, 115, 116, 125, 127, 129, 132, 136, 143, 144, 145, 147,149, 151, 155, 159, 161, 163, 164, 165, 172, 173, 175, 176, 181, 182,183, 185, 187, 190, 192, 195, 196, 197, 198, 199, 203, 0, 1, 2, 12, 13,14, 23, 28, 30, 32, 41, 42, 47, 49, 53, 61, 66, 67, 72, 73, 80, 87, 91,95, 98, 101, 103, 112, 113, 117, 126, 131, 134, 140, 146, 150, 156, 160,169, 174, 177, 178, 184, 188, 189, 191, 193, 204, 15, 43, 55, 58, 60,68, 74, 76, 81, 89, 93, 99, 102, 110, 114, 118, 133, 135, 137, 141, 148,152, 157, 170, 179, 186, 194, 205, 5, 22, 77, 82, 107, 111, 119, 128,138, 142, 153, 158, 162, 171, 180, 206, 10, 26, 45, 64, 70, 78, 84, 120,121, 139, 167, 208, 71, 122, 123, 130, 166, 210, 46, 83, 213, 124, 154,168, 200, 201, 202, 207, 209, 211, 212, 214, 215, 216, 217, 218 200 190xA2B79 199, 198, 197, 196, 195, 192, 190, 187, 185, 183, 182, 181, 176,175, 173, 172, 165, 164, 163, 161, 159, 155, 151, 149, 147, 145, 144,143, 136, 132, 129, 127, 125, 116, 115, 109, 108, 106, 105, 104, 100,97, 96, 94, 92, 90, 88, 86, 85, 79, 75, 69, 65, 63, 62, 59, 57, 56, 54,52, 51, 50, 48, 44, 40, 39, 38, 37, 36, 35, 34, 33, 31, 29, 27, 25, 24,21, 20, 19, 18, 17, 16, 11, 9, 8, 7, 6, 4, 3, 203, 193, 191, 189, 188,184, 178, 177, 174, 169, 160, 156, 150, 146, 140, 134, 131, 126, 117,113, 112, 103, 101, 98, 95, 91, 87, 80, 73, 72, 67, 66, 61, 53, 49, 47,42, 41, 32, 30, 28, 23, 14, 13, 12, 2, 1, 0, 204, 194, 186, 179, 170,157, 152, 148, 141, 137, 135, 133, 118, 114, 110, 102, 99, 93, 89, 81,76, 74, 68, 60, 58, 55, 43, 15, 205, 180, 171, 162, 158, 153, 142, 138,128, 119, 111, 107, 82, 77, 22, 5, 206, 167, 139, 121, 120, 84, 78, 70,64, 45, 26, 10, 208, 166, 130, 123, 122, 71, 210, 83, 46, 213, 124, 154,168, 200, 201, 202, 207, 209, 211, 212, 214, 215, 216, 217, 218 200 200x191513 2, 3, 6, 10, 11, 15, 17, 18, 19, 21, 26, 27, 31, 32, 33, 36,38, 40, 42, 44, 45, 48, 49, 50, 51, 53, 54, 58, 61, 62, 68, 69, 72, 73,78, 80, 81, 83, 85, 88, 89, 90, 93, 94, 95, 96, 100, 101, 103, 105, 107,108, 110, 111, 112, 114, 115, 116, 118, 121, 124, 126, 127, 130, 132,133, 134, 139, 140, 141, 142, 143, 144, 146, 148, 149, 153, 154, 155,156, 158, 160, 161, 164, 169, 176, 178, 179, 180, 181, 184, 185, 186,188, 189, 193, 195, 197, 198, 199, 200, 0, 4, 7, 12, 16, 20, 22, 28, 34,37, 39, 41, 43, 46, 52, 55, 59, 63, 70, 74, 79, 82, 84, 86, 91, 97, 102,104, 106, 109, 113, 117, 119, 122, 125, 128, 131, 135, 145, 147, 150,157, 159, 162, 165, 170, 177, 182, 187, 190, 194, 196, 201, 1, 5, 8, 13,23, 29, 35, 47, 56, 60, 64, 71, 75, 87, 92, 98, 120, 123, 129, 136, 151,163, 166, 171, 183, 191, 202, 9, 14, 24, 30, 57, 65, 76, 99, 137, 152,167, 172, 192, 203, 25, 66, 77, 138, 168, 173, 204, 67, 174, 205, 175,206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 20020 0x191513 199, 198, 197, 195, 193, 189, 188, 186, 185, 184, 181, 180,179, 178, 176, 169, 164, 161, 160, 158, 156, 155, 154, 153, 149, 148,146, 144, 143, 142, 141, 140, 139, 134, 133, 132, 130, 127, 126, 124,121, 118, 116, 115, 114, 112, 111, 110, 108, 107, 105, 103, 101, 100,96, 95, 94, 93, 90, 89, 88, 85, 83, 81, 80, 78, 73, 72, 69, 68, 62, 61,58, 54, 53, 51, 50, 49, 48, 45, 44, 42, 40, 38, 36, 33, 32, 31, 27, 26,21, 19, 18, 17, 15, 11, 10, 6, 3, 2, 200, 196, 194, 190, 187, 182, 177,170, 165, 162, 159, 157, 150, 147, 145, 135, 131, 128, 125, 122, 119,117, 113, 109, 106, 104, 102, 97, 91, 86, 84, 82, 79, 74, 70, 63, 59,55, 52, 46, 43, 41, 39, 37, 34, 28, 22, 20, 16, 12, 7, 4, 0, 201, 191,183, 171, 166, 163, 151, 136, 129, 123, 120, 98, 92, 87, 75, 71, 64, 60,56, 47, 35, 29, 23, 13, 8, 5, 1, 202, 192, 172, 167, 152, 137, 99, 76,65, 57, 30, 24, 14, 9, 203, 173, 168, 138, 77, 66, 25, 204, 174, 67,205, 175, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217,218, 219 200 21 0x2E2A69 1, 5, 6, 8, 9, 10, 12, 14, 15, 17, 19, 21, 23,26, 27, 28, 29, 30, 32, 33, 35, 39, 41, 47, 49, 51, 52, 53, 55, 58, 59,60, 61, 63, 66, 69, 72, 74, 76, 78, 79, 83, 87, 88, 89, 94, 96, 97, 101,103, 105, 108, 109, 110, 111, 113, 114, 118, 125, 127, 131, 133, 134,135, 136, 137, 138, 141, 142, 147, 150, 151, 156, 159, 160, 162, 163,164, 168, 170, 171, 172, 173, 174, 177, 180, 181, 182, 184, 188, 190,195, 197, 200, 0, 2, 7, 11, 13, 16, 18, 20, 22, 24, 31, 34, 36, 40, 42,48, 50, 54, 56, 62, 64, 67, 70, 73, 75, 77, 80, 84, 90, 95, 98, 102,104, 106, 112, 115, 119, 126, 128, 132, 139, 143, 148, 152, 157, 161,165, 169, 175, 178, 183, 185, 189, 191, 196, 198, 201, 3, 25, 37, 43,57, 65, 68, 71, 81, 85, 91, 99, 107, 116, 120, 129, 140, 144, 149, 153,158, 166, 176, 179, 186, 192, 199, 202, 4, 38, 44, 82, 86, 92, 100, 117,121, 130, 145, 154, 167, 187, 193, 203, 45, 93, 122, 146, 155, 194, 204,46, 123, 205, 124, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215,216, 217, 218, 219, 220 200 21 0x2E2A69 197, 195, 190, 188, 184, 182,181, 180, 177, 174, 173, 172, 171, 170, 168, 164, 163, 162, 160, 159,156, 151, 150, 147, 142, 141, 138, 137, 136, 135, 134, 133, 131, 127,125, 118, 114, 113, 111, 110, 109, 108, 105, 103, 101, 97, 96, 94, 89,88, 87, 83, 79, 78, 76, 74, 72, 69, 66, 63, 61, 60, 59, 58, 55, 53, 52,51, 49, 47, 41, 39, 35, 33, 32, 30, 29, 28, 27, 26, 23, 21, 19, 17, 15,14, 12, 10, 9, 8, 6, 5, 1, 200, 198, 196, 191, 189, 185, 183, 178, 175,169, 165, 161, 157, 152, 148, 143, 139, 132, 128, 126, 119, 115, 112,106, 104, 102, 98, 95, 90, 84, 80, 77, 75, 73, 70, 67, 64, 62, 56, 54,50, 48, 42, 40, 36, 34, 31, 24, 22, 20, 18, 16, 13, 11, 7, 2, 0, 201,199, 192, 186, 179, 176, 166, 158, 153, 149, 144, 140, 129, 120, 116,107, 99, 91, 85, 81, 71, 68, 65, 57, 43, 37, 25, 3, 202, 193, 187, 167,154, 145, 130, 121, 117, 100, 92, 86, 82, 44, 38, 4, 203, 194, 155, 146,122, 93, 45, 204, 123, 46, 205, 124, 206, 207, 208, 209, 210, 211, 212,213, 214, 215, 216, 217, 218, 219, 220 200 22 0x552A55 1, 2, 3, 4, 12,14, 15, 17, 19, 20, 22, 24, 27, 30, 34, 35, 36, 37, 38, 39, 40, 41, 44,45, 48, 49, 50, 51, 52, 56, 57, 58, 60, 61, 62, 65, 67, 68, 69, 72, 74,75, 76, 80, 81, 82, 84, 85, 86, 87, 92, 93, 95, 102, 105, 106, 107, 108,110, 111, 113, 116, 117, 119, 121, 122, 125, 129, 130, 131, 132, 134,136, 138, 141, 142, 147, 148, 149, 150, 152, 159, 161, 165, 169, 170,171, 172, 174, 175, 180, 182, 183, 185, 189, 190, 191, 192, 198, 200, 5,13, 16, 18, 21, 23, 25, 28, 31, 42, 46, 53, 59, 63, 66, 70, 73, 77, 83,88, 94, 96, 103, 109, 112, 114, 118, 120, 123, 126, 133, 135, 137, 139,143, 151, 153, 160, 162, 166, 173, 176, 181, 184, 186, 193, 199, 201, 6,26, 29, 32, 43, 47, 54, 64, 71, 78, 89, 97, 104, 115, 124, 127, 140,144, 154, 163, 167, 177, 187, 194, 202, 0, 7, 33, 55, 79, 90, 98, 128,145, 155, 164, 168, 178, 188, 195, 203, 8, 91, 99, 146, 156, 179, 196,204, 9, 100, 157, 197, 205, 10, 101, 158, 206, 11, 207, 208, 209, 210,211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 200 22 0x552A55198, 192, 191, 190, 189, 185, 183, 182, 180, 175, 174, 172, 171, 170,169, 165, 161, 159, 152, 150, 149, 148, 147, 142, 141, 138, 136, 134,132, 131, 130, 129, 125, 122, 121, 119, 117, 116, 113, 111, 110, 108,107, 106, 105, 102, 95, 93, 92, 87, 86, 85, 84, 82, 81, 80, 76, 75, 74,72, 69, 68, 67, 65, 62, 61, 60, 58, 57, 56, 52, 51, 50, 49, 48, 45, 44,41, 40, 39, 38, 37, 36, 35, 34, 30, 27, 24, 22, 20, 19, 17, 15, 14, 12,4, 3, 2, 1, 200, 199, 193, 186, 184, 181, 176, 173, 166, 162, 160, 153,151, 143, 139, 137, 135, 133, 126, 123, 120, 118, 114, 112, 109, 103,96, 94, 88, 83, 77, 73, 70, 66, 63, 59, 53, 46, 42, 31, 28, 25, 23, 21,18, 16, 13, 5, 201, 194, 187, 177, 167, 163, 154, 144, 140, 127, 124,115, 104, 97, 89, 78, 71, 64, 54, 47, 43, 32, 29, 26, 6, 202, 195, 188,178, 168, 164, 155, 145, 128, 98, 90, 79, 55, 33, 7, 0, 203, 196, 179,156, 146, 99, 91, 8, 204, 197, 157, 100, 9, 205, 158, 101, 10, 206, 11,207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,221 200 23 0x86F4A1 1, 3, 4, 5, 11, 12, 13, 14, 18, 20, 23, 24, 25, 28,30, 31, 32, 33, 37, 39, 42, 45, 46, 47, 49, 50, 51, 53, 55, 57, 59, 60,61, 64, 65, 67, 69, 70, 71, 72, 73, 74, 75, 77, 80, 83, 84, 85, 86, 87,88, 89, 90, 93, 94, 99, 101, 102, 104, 106, 109, 111, 112, 113, 115,116, 119, 121, 123, 124, 133, 134, 135, 137, 139, 140, 141, 142, 144,145, 148, 149, 152, 153, 154, 157, 159, 162, 164, 166, 168, 169, 175,176, 178, 179, 180, 181, 182, 187, 188, 193, 195, 200, 0, 2, 6, 15, 19,21, 26, 29, 34, 38, 40, 43, 48, 52, 54, 56, 58, 62, 66, 68, 76, 78, 81,91, 95, 100, 103, 105, 107, 110, 114, 117, 120, 122, 125, 136, 138, 143,146, 150, 155, 158, 160, 163, 165, 167, 170, 177, 183, 189, 194, 196,201, 7, 16, 22, 27, 35, 41, 44, 63, 79, 82, 92, 96, 108, 118, 126, 147,151, 156, 161, 171, 184, 190, 197, 202, 8, 17, 36, 97, 127, 172, 185,191, 198, 203, 9, 98, 128, 173, 186, 192, 199, 204, 10, 129, 174, 205,130, 206, 131, 207, 132, 208, 209, 210, 211, 212, 213, 214, 215, 216,217, 218, 219, 220, 221, 222 200 23 0x86F4A1 195, 193, 188, 187, 182,181, 180, 179, 178, 176, 175, 169, 168, 166, 164, 162, 159, 157, 154,153, 152, 149, 148, 145, 144, 142, 141, 140, 139, 137, 135, 134, 133,124, 123, 121, 119, 116, 115, 113, 112, 111, 109, 106, 104, 102, 101,99, 94, 93, 90, 89, 88, 87, 86, 85, 84, 83, 80, 77, 75, 74, 73, 72, 71,70, 69, 67, 65, 64, 61, 60, 59, 57, 55, 53, 51, 50, 49, 47, 46, 45, 42,39, 37, 33, 32, 31, 30, 28, 25, 24, 23, 20, 18, 14, 13, 12, 11, 5, 4, 3,1, 200, 196, 194, 189, 183, 177, 170, 167, 165, 163, 160, 158, 155, 150,146, 143, 138, 136, 125, 122, 120, 117, 114, 110, 107, 105, 103, 100,95, 91, 81, 78, 76, 68, 66, 62, 58, 56, 54, 52, 48, 43, 40, 38, 34, 29,26, 21, 19, 15, 6, 2, 0, 201, 197, 190, 184, 171, 161, 156, 151, 147,126, 118, 108, 96, 92, 82, 79, 63, 44, 41, 35, 27, 22, 16, 7, 202, 198,191, 185, 172, 127, 97, 36, 17, 8, 203, 199, 192, 186, 173, 128, 98, 9,204, 174, 129, 10, 205, 130, 206, 131, 207, 132, 208, 209, 210, 211,212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222 200 24 0x1D11A9B0, 2, 3, 5, 6, 8, 11, 12, 13, 16, 19, 20, 22, 24, 28, 32, 33, 35, 37,38, 39, 40, 41, 42, 44, 46, 47, 49, 50, 54, 55, 57, 59, 60, 62, 64, 67,69, 74, 79, 80, 84, 85, 86, 88, 91, 94, 102, 105, 109, 110, 111, 113,114, 116, 118, 119, 121, 122, 125, 126, 127, 129, 130, 131, 132, 136,137, 141, 142, 143, 147, 148, 149, 151, 153, 155, 158, 161, 164, 166,168, 170, 171, 173, 175, 178, 179, 180, 182, 183, 186, 187, 189, 192,194, 198, 199, 200, 1, 4, 7, 9, 14, 17, 21, 23, 25, 29, 34, 36, 43, 45,48, 51, 56, 58, 61, 63, 65, 68, 70, 75, 81, 87, 89, 92, 95, 103, 106,112, 115, 117, 120, 123, 128, 133, 138, 144, 150, 152, 154, 156, 159,162, 165, 167, 169, 172, 174, 176, 181, 184, 188, 190, 193, 195, 201,10, 15, 18, 26, 30, 52, 66, 71, 76, 82, 90, 93, 96, 104, 107, 124, 134,139, 145, 157, 160, 163, 177, 185, 191, 196, 202, 27, 31, 53, 72, 77,83, 97, 108, 135, 140, 146, 197, 203, 73, 78, 98, 204, 99, 205, 100,206, 101, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218,219, 220, 221, 222, 223 200 24 0x1D11A9B 199, 198, 194, 192, 189, 187,186, 183, 182, 180, 179, 178, 175, 173, 171, 170, 168, 166, 164, 161,158, 155, 153, 151, 149, 148, 147, 143, 142, 141, 137, 136, 132, 131,130, 129, 127, 126, 125, 122, 121, 119, 118, 116, 114, 113, 111, 110,109, 105, 102, 94, 91, 88, 86, 85, 84, 80, 79, 74, 69, 67, 64, 62, 60,59, 57, 55, 54, 50, 49, 47, 46, 44, 42, 41, 40, 39, 38, 37, 35, 33, 32,28, 24, 22, 20, 19, 16, 13, 12, 11, 8, 6, 5, 3, 2, 0, 200, 195, 193,190, 188, 184, 181, 176, 174, 172, 169, 167, 165, 162, 159, 156, 154,152, 150, 144, 138, 133, 128, 123, 120, 117, 115, 112, 106, 103, 95, 92,89, 87, 81, 75, 70, 68, 65, 63, 61, 58, 56, 51, 48, 45, 43, 36, 34, 29,25, 23, 21, 17, 14, 9, 7, 4, 1, 201, 196, 191, 185, 177, 163, 160, 157,145, 139, 134, 124, 107, 104, 96, 93, 90, 82, 76, 71, 66, 52, 30, 26,18, 15, 10, 202, 197, 146, 140, 135, 108, 97, 83, 77, 72, 53, 31, 27,203, 98, 78, 73, 204, 99, 205, 100, 206, 101, 207, 208, 209, 210, 211,212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223 1000 11 0x94F0, 1, 4, 5, 6, 8, 13, 14, 15, 17, 18, 22, 24, 26, 29, 30, 32, 33, 34,38, 39, 40, 43, 44, 47, 50, 52, 53, 58, 59, 62, 63, 65, 67, 72, 73, 75,76, 78, 79, 82, 85, 86, 88, 89, 90, 91, 95, 97, 100, 104, 105, 108, 112,113, 115, 116, 118, 124, 126, 127, 128, 129, 130, 132, 133, 134, 135,141, 142, 145, 147, 148, 149, 151, 153, 154, 156, 159, 161, 164, 167,168, 169, 170, 173, 175, 176, 177, 181, 185, 189, 191, 193, 194, 195,196, 198, 200, 202, 203, 205, 207, 211, 212, 213, 214, 215, 217, 218,222, 223, 224, 228, 230, 231, 232, 233, 234, 235, 236, 237, 239, 240,241, 243, 245, 246, 247, 248, 250, 251, 252, 255, 256, 267, 270, 272,273, 275, 279, 280, 281, 282, 285, 288, 289, 290, 292, 295, 297, 299,300, 302, 303, 306, 307, 309, 314, 320, 322, 324, 325, 330, 335, 336,343, 346, 347, 348, 349, 350, 351, 352, 353, 356, 357, 358, 359, 360,362, 364, 366, 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1008, 265, 637, 1009, 266, 638, 1010 1000 11 0x94F 999, 996, 995,994, 992, 991, 990, 989, 987, 985, 984, 983, 981, 980, 979, 978, 977,976, 975, 974, 972, 968, 967, 966, 962, 961, 959, 958, 957, 956, 955,951, 949, 947, 946, 944, 942, 940, 939, 938, 937, 935, 933, 929, 925,921, 920, 919, 917, 914, 913, 912, 911, 908, 905, 903, 900, 898, 897,895, 893, 892, 891, 889, 886, 885, 879, 878, 877, 876, 874, 873, 872,871, 870, 868, 862, 860, 859, 857, 856, 852, 849, 848, 844, 841, 839,835, 834, 833, 832, 830, 829, 826, 823, 822, 820, 819, 817, 816, 811,809, 807, 806, 803, 802, 797, 796, 794, 791, 788, 787, 784, 783, 782,778, 777, 776, 774, 773, 770, 768, 766, 762, 761, 759, 758, 757, 752,750, 749, 748, 745, 744, 743, 742, 741, 738, 736, 734, 732, 731, 730,729, 728, 725, 724, 723, 722, 721, 720, 719, 718, 715, 708, 707, 702,697, 696, 694, 692, 686, 681, 679, 678, 675, 674, 672, 671, 669, 667,664, 662, 661, 660, 657, 654, 653, 652, 651, 647, 645, 644, 642, 639,628, 627, 624, 623, 622, 620, 619, 618, 617, 615, 613, 612, 611, 609,608, 607, 606, 605, 604, 603, 602, 600, 596, 595, 594, 590, 589, 587,586, 585, 584, 583, 579, 577, 575, 574, 572, 570, 568, 567, 566, 565,563, 561, 557, 553, 549, 548, 547, 545, 542, 541, 540, 539, 536, 533,531, 528, 526, 525, 523, 521, 520, 519, 517, 514, 513, 507, 506, 505,504, 502, 501, 500, 499, 498, 496, 490, 488, 487, 485, 484, 480, 477,476, 472, 469, 467, 463, 462, 461, 460, 458, 457, 454, 451, 450, 448,447, 445, 444, 439, 437, 435, 434, 431, 430, 425, 424, 422, 419, 416,415, 412, 411, 410, 406, 405, 404, 402, 401, 398, 396, 394, 390, 389,387, 386, 385, 380, 378, 377, 376, 373, 372, 371, 370, 369, 366, 364,362, 360, 359, 358, 357, 356, 353, 352, 351, 350, 349, 348, 347, 346,343, 336, 335, 330, 325, 324, 322, 320, 314, 309, 307, 306, 303, 302,300, 299, 297, 295, 292, 290, 289, 288, 285, 282, 281, 280, 279, 275,273, 272, 270, 267, 256, 255, 252, 251, 250, 248, 247, 246, 245, 243,241, 240, 239, 237, 236, 235, 234, 233, 232, 231, 230, 228, 224, 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591, 588, 580, 578, 576, 573, 571, 569, 564,562, 558, 554, 550, 546, 543, 537, 534, 532, 529, 527, 524, 522, 518,515, 508, 503, 497, 491, 489, 486, 481, 478, 473, 470, 468, 464, 459,455, 452, 449, 446, 440, 438, 436, 432, 426, 423, 420, 417, 413, 407,403, 399, 397, 395, 391, 388, 381, 379, 374, 367, 365, 363, 361, 354,344, 337, 331, 326, 323, 321, 315, 310, 308, 304, 301, 298, 296, 293,291, 286, 283, 276, 274, 271, 268, 257, 253, 249, 244, 242, 238, 229,225, 219, 216, 208, 206, 204, 201, 199, 197, 192, 190, 186, 182, 178,174, 171, 165, 162, 160, 157, 155, 152, 150, 146, 143, 136, 131, 125,119, 117, 114, 109, 106, 101, 98, 96, 92, 87, 83, 80, 77, 74, 68, 66,64, 60, 54, 51, 48, 45, 41, 35, 31, 27, 25, 23, 19, 16, 9, 7, 2, 1001,998, 970, 964, 953, 931, 927, 923, 916, 910, 907, 902, 888, 881, 864,854, 851, 846, 843, 837, 828, 825, 813, 805, 799, 793, 790, 786, 780,772, 764, 754, 747, 740, 727, 717, 710, 704, 699, 688, 683, 677, 666,659, 656, 649, 641, 630, 626, 598, 592, 581, 559, 555, 551, 544, 538,535, 530, 516, 509, 492, 482, 479, 474, 471, 465, 456, 453, 441, 433,427, 421, 418, 414, 408, 400, 392, 382, 375, 368, 355, 345, 338, 332,327, 316, 311, 305, 294, 287, 284, 277, 269, 258, 254, 226, 220, 209,187, 183, 179, 172, 166, 163, 158, 144, 137, 120, 110, 107, 102, 99, 93,84, 81, 69, 61, 55, 49, 46, 42, 36, 28, 20, 10, 3, 1002, 971, 965, 954,932, 928, 924, 882, 865, 855, 847, 838, 814, 800, 781, 765, 755, 711,705, 700, 689, 684, 650, 631, 599, 593, 582, 560, 556, 552, 510, 493,483, 475, 466, 442, 428, 409, 393, 383, 339, 333, 328, 317, 312, 278,259, 227, 221, 210, 188, 184, 180, 138, 121, 111, 103, 94, 70, 56, 37,21, 11, 1003, 883, 866, 815, 801, 756, 712, 706, 701, 690, 685, 632,511, 494, 443, 429, 384, 340, 334, 329, 318, 313, 260, 139, 122, 71, 57,12, 1004, 884, 867, 713, 691, 633, 512, 495, 341, 319, 261, 140, 123,1005, 714, 634, 342, 262, 1006, 635, 263, 1007, 636, 264, 1008, 637,265, 1009, 638, 266, 1010 22 3 0xD 1, 4, 5, 6, 8, 11, 12, 13, 0, 19, 2,3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24 22 3 0xD 4, 5, 6, 8,1, 12, 11, 13, 2, 19, 0, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23,17, 24 22 3 0xD 1, 4, 5, 6, 8, 12, 11, 13, 0, 19, 2, 3, 15, 18, 20, 7,9, 22, 10, 21, 16, 14, 23, 17, 24 22 3 0xD 1, 4, 5, 6, 12, 11, 13, 8, 0,19, 2, 3, 15, 18, 20, 7, 9, 22, 10, 21, 16, 14, 23, 17, 24


12. The apparatus according to claim 7, wherein the maximum-lengthinterleaving sequence is any sequence in the following table: CRCInterleaving sequence for which reverse-order numbering is K_(max) Lpolynomial used 200 19 0xA2B79 2, 3, 4, 10, 12, 13, 16, 17, 21, 24, 26,30, 33, 36, 37, 38, 40, 47, 50, 51, 54, 55, 59, 62, 65, 66, 68, 69, 70,71, 72, 74, 86, 87, 89, 90, 92, 94, 95, 96, 99, 105, 106, 109, 110, 113,114, 123, 126, 127, 129, 130, 132, 135, 137, 138, 139, 141, 142, 143,144, 147, 148, 152, 154, 155, 157, 160, 162, 164, 166, 168, 173, 175,176, 177, 179, 180, 181, 185, 186, 188, 189, 192, 193, 194, 197, 198,199, 200, 0, 1, 8, 11, 14, 15, 19, 22, 28, 31, 34, 35, 45, 48, 49, 52,53, 57, 60, 63, 64, 67, 84, 85, 88, 93, 97, 103, 104, 107, 108, 111,112, 121, 124, 125, 128, 133, 136, 140, 145, 146, 150, 153, 158, 171,174, 178, 183, 184, 187, 190, 191, 195, 196, 202, 7, 9, 18, 23, 27, 44,56, 83, 91, 102, 120, 134, 149, 151, 159, 161, 163, 165, 170, 172, 182,203, 5, 20, 29, 39, 43, 73, 77, 78, 81, 98, 100, 101, 119, 122, 131,156, 167, 209, 42, 46, 61, 76, 80, 118, 210, 6, 25, 32, 41, 58, 75, 79,82, 117, 211, 116, 169, 212, 115, 201, 204, 205, 206, 207, 208, 213,214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197, 194, 193, 192,189, 188, 186, 185, 181, 180, 179, 177, 176, 175, 173, 168, 166, 164,162, 160, 157, 155, 154, 152, 148, 147, 144, 143, 142, 141, 139, 138,137, 135, 132, 130, 129, 127, 126, 123, 114, 113, 110, 109, 106, 105,99, 96, 95, 94, 92, 90, 89, 87, 86, 74, 72, 71, 70, 69, 68, 66, 65, 62,59, 55, 54, 51, 50, 47, 40, 38, 37, 36, 33, 30, 26, 24, 21, 17, 16, 13,12, 10, 4, 3, 2, 200, 196, 195, 191, 190, 187, 184, 183, 178, 174, 171,158, 153, 150, 146, 145, 140, 136, 133, 128, 125, 124, 121, 112, 111,108, 107, 104, 103, 97, 93, 88, 85, 84, 67, 64, 63, 60, 57, 53, 52, 49,48, 45, 35, 34, 31, 28, 22, 19, 15, 14, 11, 8, 1, 0, 202, 182, 172, 170,165, 163, 161, 159, 151, 149, 134, 120, 102, 91, 83, 56, 44, 27, 23, 18,9, 7, 203, 167, 156, 131, 122, 119, 101, 100, 98, 81, 78, 77, 73, 43,39, 29, 20, 5, 209, 118, 80, 76, 61, 46, 42, 210, 117, 82, 79, 75, 58,41, 32, 25, 6, 211, 169, 116, 212, 115, 201, 204, 205, 206, 207, 208,213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2, 8, 10, 11, 14, 15,19, 22, 24, 28, 31, 34, 35, 36, 38, 45, 48, 49, 52, 53, 57, 60, 63, 64,66, 67, 68, 69, 70, 72, 84, 85, 87, 88, 90, 92, 93, 94, 97, 103, 104,107, 108, 111, 112, 121, 124, 125, 127, 128, 130, 133, 135, 136, 137,139, 140, 141, 142, 145, 146, 150, 152, 153, 155, 158, 160, 162, 164,166, 171, 173, 174, 175, 177, 178, 179, 183, 184, 186, 187, 190, 191,192, 195, 196, 197, 198, 199, 202, 3, 4, 7, 9, 12, 16, 17, 18, 23, 26,27, 40, 44, 50, 54, 55, 56, 74, 83, 91, 95, 99, 102, 105, 109, 113, 114,120, 134, 143, 147, 148, 149, 151, 159, 161, 163, 165, 168, 170, 172,180, 181, 182, 188, 193, 203, 5, 13, 20, 29, 30, 39, 42, 47, 51, 58, 59,62, 65, 73, 81, 82, 89, 96, 98, 100, 101, 106, 110, 118, 123, 131, 138,144, 156, 167, 176, 205, 6, 25, 37, 41, 46, 61, 71, 80, 117, 122, 132,169, 185, 194, 206, 43, 77, 78, 119, 129, 189, 209, 21, 32, 75, 76, 79,157, 211, 33, 116, 154, 212, 86, 115, 126, 200, 201, 204, 207, 208, 210,213, 214, 215, 216, 217, 218 200 19 0xA2B79 199, 198, 197, 196, 195,192, 191, 190, 187, 186, 184, 183, 179, 178, 177, 175, 174, 173, 171,166, 164, 162, 160, 158, 155, 153, 152, 150, 146, 145, 142, 141, 140,139, 137, 136, 135, 133, 130, 128, 127, 125, 124, 121, 112, 111, 108,107, 104, 103, 97, 94, 93, 92, 90, 88, 87, 85, 84, 72, 70, 69, 68, 67,66, 64, 63, 60, 57, 53, 52, 49, 48, 45, 38, 36, 35, 34, 31, 28, 24, 22,19, 15, 14, 11, 10, 8, 2, 1, 0, 202, 193, 188, 182, 181, 180, 172, 170,168, 165, 163, 161, 159, 151, 149, 148, 147, 143, 134, 120, 114, 113,109, 105, 102, 99, 95, 91, 83, 74, 56, 55, 54, 50, 44, 40, 27, 26, 23,18, 17, 16, 12, 9, 7, 4, 3, 203, 176, 167, 156, 144, 138, 131, 123, 118,110, 106, 101, 100, 98, 96, 89, 82, 81, 73, 65, 62, 59, 58, 51, 47, 42,39, 30, 29, 20, 13, 5, 205, 194, 185, 169, 132, 122, 117, 80, 71, 61,46, 41, 37, 25, 6, 206, 189, 129, 119, 78, 77, 43, 209, 157, 79, 76, 75,32, 21, 211, 154, 116, 33, 212, 86, 115, 126, 200, 201, 204, 207, 208,210, 213, 214, 215, 216, 217, 218 200 19 0xA2B79 0, 1, 2, 3, 4, 7, 9,12, 14, 16, 17, 18, 23, 24, 26, 27, 34, 35, 36, 38, 40, 44, 48, 50, 52,54, 55, 56, 63, 67, 70, 72, 74, 83, 84, 90, 91, 93, 94, 95, 99, 102,103, 105, 107, 109, 111, 113, 114, 120, 124, 130, 134, 136, 137, 140,142, 143, 145, 147, 148, 149, 151, 155, 159, 160, 161, 162, 163, 164,165, 166, 168, 170, 172, 174, 175, 178, 179, 180, 181, 182, 183, 188,190, 191, 192, 193, 195, 196, 203, 6, 8, 10, 11, 15, 21, 22, 25, 30, 39,43, 49, 53, 59, 65, 68, 73, 82, 86, 87, 96, 98, 101, 104, 108, 112, 119,126, 127, 132, 133, 138, 146, 150, 152, 157, 158, 167, 169, 171, 176,185, 186, 187, 197, 198, 199, 204, 5, 13, 20, 29, 42, 47, 51, 58, 62,64, 66, 81, 85, 89, 97, 100, 106, 110, 118, 123, 125, 131, 139, 141,144, 156, 184, 205, 19, 28, 37, 41, 46, 57, 61, 71, 80, 88, 92, 117,122, 177, 194, 206, 32, 60, 78, 79, 115, 121, 129, 135, 154, 173, 189,208, 33, 69, 76, 77, 128, 210, 116, 153, 213, 31, 45, 75, 200, 201, 202,207, 209, 211, 212, 214, 215, 216, 217, 218 200 19 0xA2B79 196, 195,193, 192, 191, 190, 188, 183, 182, 181, 180, 179, 178, 175, 174, 172,170, 168, 166, 165, 164, 163, 162, 161, 160, 159, 155, 151, 149, 148,147, 145, 143, 142, 140, 137, 136, 134, 130, 124, 120, 114, 113, 111,109, 107, 105, 103, 102, 99, 95, 94, 93, 91, 90, 84, 83, 74, 72, 70, 67,63, 56, 55, 54, 52, 50, 48, 44, 40, 38, 36, 35, 34, 27, 26, 24, 23, 18,17, 16, 14, 12, 9, 7, 4, 3, 2, 1, 0, 203, 199, 198, 197, 187, 186, 185,176, 171, 169, 167, 158, 157, 152, 150, 146, 138, 133, 132, 127, 126,119, 112, 108, 104, 101, 98, 96, 87, 86, 82, 73, 68, 65, 59, 53, 49, 43,39, 30, 25, 22, 21, 15, 11, 10, 8, 6, 204, 184, 156, 144, 141, 139, 131,125, 123, 118, 110, 106, 100, 97, 89, 85, 81, 66, 64, 62, 58, 51, 47,42, 29, 20, 13, 5, 205, 194, 177, 122, 117, 92, 88, 80, 71, 61, 57, 46,41, 37, 28, 19, 206, 189, 173, 154, 135, 129, 121, 115, 79, 78, 60, 32,208, 128, 77, 76, 69, 33, 210, 153, 116, 213, 31, 45, 75, 200, 201, 202,207, 209, 211, 212, 214, 215, 216, 217, 218 200 20 0x191513 0, 1, 2, 4,6, 10, 11, 13, 14, 15, 18, 19, 20, 21, 23, 30, 35, 38, 39, 41, 43, 44,45, 46, 50, 51, 53, 55, 56, 57, 58, 59, 60, 65, 66, 67, 69, 72, 73, 75,78, 81, 83, 84, 85, 87, 88, 89, 91, 92, 94, 96, 98, 99, 103, 104, 105,106, 109, 110, 111, 114, 116, 118, 119, 121, 126, 127, 130, 131, 137,138, 141, 145, 146, 148, 149, 150, 151, 154, 155, 157, 159, 161, 163,166, 167, 168, 172, 173, 178, 180, 181, 182, 184, 188, 189, 193, 196,197, 200, 3, 5, 9, 12, 17, 22, 29, 34, 37, 40, 42, 49, 52, 54, 64, 68,71, 74, 77, 80, 82, 86, 90, 93, 95, 97, 102, 108, 113, 115, 117, 120,125, 129, 136, 140, 144, 147, 153, 156, 158, 160, 162, 165, 171, 177,179, 183, 187, 192, 195, 199, 201, 8, 16, 28, 33, 36, 48, 63, 70, 76,79, 101, 107, 112, 124, 128, 135, 139, 143, 152, 164, 170, 176, 186,191, 194, 198, 202, 7, 27, 32, 47, 62, 100, 123, 134, 142, 169, 175,185, 190, 203, 26, 31, 61, 122, 133, 174, 204, 25, 132, 205, 24, 206,207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 200 200x191513 197, 196, 193, 189, 188, 184, 182, 181, 180, 178, 173, 172,168, 167, 166, 163, 161, 159, 157, 155, 154, 151, 150, 149, 148, 146,145, 141, 138, 137, 131, 130, 127, 126, 121, 119, 118, 116, 114, 111,110, 109, 106, 105, 104, 103, 99, 98, 96, 94, 92, 91, 89, 88, 87, 85,84, 83, 81, 78, 75, 73, 72, 69, 67, 66, 65, 60, 59, 58, 57, 56, 55, 53,51, 50, 46, 45, 44, 43, 41, 39, 38, 35, 30, 23, 21, 20, 19, 18, 15, 14,13, 11, 10, 6, 4, 2, 1, 0, 200, 199, 195, 192, 187, 183, 179, 177, 171,165, 162, 160, 158, 156, 153, 147, 144, 140, 136, 129, 125, 120, 117,115, 113, 108, 102, 97, 95, 93, 90, 86, 82, 80, 77, 74, 71, 68, 64, 54,52, 49, 42, 40, 37, 34, 29, 22, 17, 12, 9, 5, 3, 201, 198, 194, 191,186, 176, 170, 164, 152, 143, 139, 135, 128, 124, 112, 107, 101, 79, 76,70, 63, 48, 36, 33, 28, 16, 8, 202, 190, 185, 175, 169, 142, 134, 123,100, 62, 47, 32, 27, 7, 203, 174, 133, 122, 61, 31, 26, 204, 132, 25,205, 24, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217,218, 219 200 21 0x2E2A69 2, 4, 9, 11, 15, 17, 18, 19, 22, 25, 26, 27,28, 29, 31, 35, 36, 37, 39, 40, 43, 48, 49, 52, 57, 58, 61, 62, 63, 64,65, 66, 68, 72, 74, 81, 85, 86, 88, 89, 90, 91, 94, 96, 98, 102, 103,105, 110, 111, 112, 116, 120, 121, 123, 125, 127, 130, 133, 136, 138,139, 140, 141, 144, 146, 147, 148, 150, 152, 158, 160, 164, 166, 167,169, 170, 171, 172, 173, 176, 178, 180, 182, 184, 185, 187, 189, 190,191, 193, 194, 198, 200, 1, 3, 8, 10, 14, 16, 21, 24, 30, 34, 38, 42,47, 51, 56, 60, 67, 71, 73, 80, 84, 87, 93, 95, 97, 101, 104, 109, 115,119, 122, 124, 126, 129, 132, 135, 137, 143, 145, 149, 151, 157, 159,163, 165, 168, 175, 177, 179, 181, 183, 186, 188, 192, 197, 199, 201, 0,7, 13, 20, 23, 33, 41, 46, 50, 55, 59, 70, 79, 83, 92, 100, 108, 114,118, 128, 131, 134, 142, 156, 162, 174, 196, 202, 6, 12, 32, 45, 54, 69,78, 82, 99, 107, 113, 117, 155, 161, 195, 203, 5, 44, 53, 77, 106, 154,204, 76, 153, 205, 75, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215,216, 217, 218, 219, 220 200 21 0x2E2A69 198, 194, 193, 191, 190, 189,187, 185, 184, 182, 180, 178, 176, 173, 172, 171, 170, 169, 167, 166,164, 160, 158, 152, 150, 148, 147, 146, 144, 141, 140, 139, 138, 136,133, 130, 127, 125, 123, 121, 120, 116, 112, 111, 110, 105, 103, 102,98, 96, 94, 91, 90, 89, 88, 86, 85, 81, 74, 72, 68, 66, 65, 64, 63, 62,61, 58, 57, 52, 49, 48, 43, 40, 39, 37, 36, 35, 31, 29, 28, 27, 26, 25,22, 19, 18, 17, 15, 11, 9, 4, 2, 200, 199, 197, 192, 188, 186, 183, 181,179, 177, 175, 168, 165, 163, 159, 157, 151, 149, 145, 143, 137, 135,132, 129, 126, 124, 122, 119, 115, 109, 104, 101, 97, 95, 93, 87, 84,80, 73, 71, 67, 60, 56, 51, 47, 42, 38, 34, 30, 24, 21, 16, 14, 10, 8,3, 1, 201, 196, 174, 162, 156, 142, 134, 131, 128, 118, 114, 108, 100,92, 83, 79, 70, 59, 55, 50, 46, 41, 33, 23, 20, 13, 7, 0, 202, 195, 161,155, 117, 113, 107, 99, 82, 78, 69, 54, 45, 32, 12, 6, 203, 154, 106,77, 53, 44, 5, 204, 153, 76, 205, 75, 206, 207, 208, 209, 210, 211, 212,213, 214, 215, 216, 217, 218, 219, 220 200 22 0x552A55 1, 7, 8, 9, 10,14, 16, 17, 19, 24, 25, 27, 28, 29, 30, 34, 38, 40, 47, 49, 50, 51, 52,57, 58, 61, 63, 65, 67, 68, 69, 70, 74, 77, 78, 80, 82, 83, 86, 88, 89,91, 92, 93, 94, 97, 104, 106, 107, 112, 113, 114, 115, 117, 118, 119,123, 124, 125, 127, 130, 131, 132, 134, 137, 138, 139, 141, 142, 143,147, 148, 149, 150, 151, 154, 155, 158, 159, 160, 161, 162, 163, 164,165, 169, 172, 175, 177, 179, 180, 182, 184, 185, 187, 195, 196, 197,198, 200, 0, 6, 13, 15, 18, 23, 26, 33, 37, 39, 46, 48, 56, 60, 62, 64,66, 73, 76, 79, 81, 85, 87, 90, 96, 103, 105, 111, 116, 122, 126, 129,133, 136, 140, 146, 153, 157, 168, 171, 174, 176, 178, 181, 183, 186,194, 201, 5, 12, 22, 32, 36, 45, 55, 59, 72, 75, 84, 95, 102, 110, 121,128, 135, 145, 152, 156, 167, 170, 173, 193, 202, 4, 11, 21, 31, 35, 44,54, 71, 101, 109, 120, 144, 166, 192, 199, 203, 3, 20, 43, 53, 100, 108,191, 204, 2, 42, 99, 190, 205, 41, 98, 189, 206, 188, 207, 208, 209,210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221 200 220x552A55 198, 197, 196, 195, 187, 185, 184, 182, 180, 179, 177, 175,172, 169, 165, 164, 163, 162, 161, 160, 159, 158, 155, 154, 151, 150,149, 148, 147, 143, 142, 141, 139, 138, 137, 134, 132, 131, 130, 127,125, 124, 123, 119, 118, 117, 115, 114, 113, 112, 107, 106, 104, 97, 94,93, 92, 91, 89, 88, 86, 83, 82, 80, 78, 77, 74, 70, 69, 68, 67, 65, 63,61, 58, 57, 52, 51, 50, 49, 47, 40, 38, 34, 30, 29, 28, 27, 25, 24, 19,17, 16, 14, 10, 9, 8, 7, 1, 200, 194, 186, 183, 181, 178, 176, 174, 171,168, 157, 153, 146, 140, 136, 133, 129, 126, 122, 116, 111, 105, 103,96, 90, 87, 85, 81, 79, 76, 73, 66, 64, 62, 60, 56, 48, 46, 39, 37, 33,26, 23, 18, 15, 13, 6, 0, 201, 193, 173, 170, 167, 156, 152, 145, 135,128, 121, 110, 102, 95, 84, 75, 72, 59, 55, 45, 36, 32, 22, 12, 5, 202,199, 192, 166, 144, 120, 109, 101, 71, 54, 44, 35, 31, 21, 11, 4, 203,191, 108, 100, 53, 43, 20, 3, 204, 190, 99, 42, 2, 205, 189, 98, 41,206, 188, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218,219, 220, 221 200 23 0x86F4A1 4, 6, 11, 12, 17, 18, 19, 20, 21, 23, 24,30, 31, 33, 35, 37, 40, 42, 45, 46, 47, 50, 51, 54, 55, 57, 58, 59, 60,62, 64, 65, 66, 75, 76, 78, 80, 83, 84, 86, 87, 88, 90, 93, 95, 97, 98,100, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 119, 122, 124,125, 126, 127, 128, 129, 130, 132, 134, 135, 138, 139, 140, 142, 144,146, 148, 149, 150, 152, 153, 154, 157, 160, 162, 166, 167, 168, 169,171, 174, 175, 176, 179, 181, 185, 186, 187, 188, 194, 195, 196, 198,200, 3, 5, 10, 16, 22, 29, 32, 34, 36, 39, 41, 44, 49, 53, 56, 61, 63,74, 77, 79, 82, 85, 89, 92, 94, 96, 99, 104, 108, 118, 121, 123, 131,133, 137, 141, 143, 145, 147, 151, 156, 159, 161, 165, 170, 173, 178,180, 184, 193, 197, 199, 201, 2, 9, 15, 28, 38, 43, 48, 52, 73, 81, 91,103, 107, 117, 120, 136, 155, 158, 164, 172, 177, 183, 192, 202, 1, 8,14, 27, 72, 102, 163, 182, 191, 203, 0, 7, 13, 26, 71, 101, 190, 204,25, 70, 189, 205, 69, 206, 68, 207, 67, 208, 209, 210, 211, 212, 213,214, 215, 216, 217, 218, 219, 220, 221, 222 200 23 0x86F4A1 198, 196,195, 194, 188, 187, 186, 185, 181, 179, 176, 175, 174, 171, 169, 168,167, 166, 162, 160, 157, 154, 153, 152, 150, 149, 148, 146, 144, 142,140, 139, 138, 135, 134, 132, 130, 129, 128, 127, 126, 125, 124, 122,119, 116, 115, 114, 113, 112, 111, 110, 109, 106, 105, 100, 98, 97, 95,93, 90, 88, 87, 86, 84, 83, 80, 78, 76, 75, 66, 65, 64, 62, 60, 59, 58,57, 55, 54, 51, 50, 47, 46, 45, 42, 40, 37, 35, 33, 31, 30, 24, 23, 21,20, 19, 18, 17, 12, 11, 6, 4, 200, 199, 197, 193, 184, 180, 178, 173,170, 165, 161, 159, 156, 151, 147, 145, 143, 141, 137, 133, 131, 123,121, 118, 108, 104, 99, 96, 94, 92, 89, 85, 82, 79, 77, 74, 63, 61, 56,53, 49, 44, 41, 39, 36, 34, 32, 29, 22, 16, 10, 5, 3, 201, 192, 183,177, 172, 164, 158, 155, 136, 120, 117, 107, 103, 91, 81, 73, 52, 48,43, 38, 28, 15, 9, 2, 202, 191, 182, 163, 102, 72, 27, 14, 8, 1, 203,190, 101, 71, 26, 13, 7, 0, 204, 189, 70, 25, 205, 69, 206, 68, 207, 67,208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221,222 200 24 0x1D11A9B 0, 1, 5, 7, 10, 12, 13, 16, 17, 19, 20, 21, 24, 26,28, 29, 31, 33, 35, 38, 41, 44, 46, 48, 50, 51, 52, 56, 57, 58, 62, 63,67, 68, 69, 70, 72, 73, 74, 77, 78, 80, 81, 83, 85, 86, 88, 89, 90, 94,97, 105, 108, 111, 113, 114, 115, 119, 120, 125, 130, 132, 135, 137,139, 140, 142, 144, 145, 149, 150, 152, 153, 155, 157, 158, 159, 160,161, 162, 164, 166, 167, 171, 175, 177, 179, 180, 183, 186, 187, 188,191, 193, 194, 196, 197, 199, 200, 4, 6, 9, 11, 15, 18, 23, 25, 27, 30,32, 34, 37, 40, 43, 45, 47, 49, 55, 61, 66, 71, 76, 79, 82, 84, 87, 93,96, 104, 107, 110, 112, 118, 124, 129, 131, 134, 136, 138, 141, 143,148, 151, 154, 156, 163, 165, 170, 174, 176, 178, 182, 185, 190, 192,195, 198, 201, 3, 8, 14, 22, 36, 39, 42, 54, 60, 65, 75, 92, 95, 103,106, 109, 117, 123, 128, 133, 147, 169, 173, 181, 184, 189, 202, 2, 53,59, 64, 91, 102, 116, 122, 127, 146, 168, 172, 203, 101, 121, 126, 204,100, 205, 99, 206, 98, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216,217, 218, 219, 220, 221, 222, 223 200 24 0x1D11A9B 199, 197, 196, 194,193, 191, 188, 187, 186, 183, 180, 179, 177, 175, 171, 167, 166, 164,162, 161, 160, 159, 158, 157, 155, 153, 152, 150, 149, 145, 144, 142,140, 139, 137, 135, 132, 130, 125, 120, 119, 115, 114, 113, 111, 108,105, 97, 94, 90, 89, 88, 86, 85, 83, 81, 80, 78, 77, 74, 73, 72, 70, 69,68, 67, 63, 62, 58, 57, 56, 52, 51, 50, 48, 46, 44, 41, 38, 35, 33, 31,29, 28, 26, 24, 21, 20, 19, 17, 16, 13, 12, 10, 7, 5, 1, 0, 200, 198,195, 192, 190, 185, 182, 178, 176, 174, 170, 165, 163, 156, 154, 151,148, 143, 141, 138, 136, 134, 131, 129, 124, 118, 112, 110, 107, 104,96, 93, 87, 84, 82, 79, 76, 71, 66, 61, 55, 49, 47, 45, 43, 40, 37, 34,32, 30, 27, 25, 23, 18, 15, 11, 9, 6, 4, 201, 189, 184, 181, 173, 169,147, 133, 128, 123, 117, 109, 106, 103, 95, 92, 75, 65, 60, 54, 42, 39,36, 22, 14, 8, 3, 202, 172, 168, 146, 127, 122, 116, 102, 91, 64, 59,53, 2, 203, 126, 121, 101, 204, 100, 205, 99, 206, 98, 207, 208, 209,210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 2231000 11 0x94F 0, 3, 4, 5, 7, 8, 9, 10, 12, 14, 15, 16, 18, 19, 20, 21,22, 23, 24, 25, 27, 31, 32, 33, 37, 38, 40, 41, 42, 43, 44, 48, 50, 52,53, 55, 57, 59, 60, 61, 62, 64, 66, 70, 74, 78, 79, 80, 82, 85, 86, 87,88, 91, 94, 96, 99, 101, 102, 104, 106, 107, 108, 110, 113, 114, 120,121, 122, 123, 125, 126, 127, 128, 129, 131, 137, 139, 140, 142, 143,147, 150, 151, 155, 158, 160, 164, 165, 166, 167, 169, 170, 173, 176,177, 179, 180, 182, 183, 188, 190, 192, 193, 196, 197, 202, 203, 205,208, 211, 212, 215, 216, 217, 221, 222, 223, 225, 226, 229, 231, 233,237, 238, 240, 241, 242, 247, 249, 250, 251, 254, 255, 256, 257, 258,261, 263, 265, 267, 268, 269, 270, 271, 274, 275, 276, 277, 278, 279,280, 281, 284, 291, 292, 297, 302, 303, 305, 307, 313, 318, 320, 321,324, 325, 327, 328, 330, 332, 335, 337, 338, 339, 342, 345, 346, 347,348, 352, 354, 355, 357, 360, 371, 372, 375, 376, 377, 379, 380, 381,382, 384, 386, 387, 388, 390, 391, 392, 393, 394, 395, 396, 397, 399,403, 404, 405, 409, 410, 412, 413, 414, 415, 416, 420, 422, 424, 425,427, 429, 431, 432, 433, 434, 436, 438, 442, 446, 450, 451, 452, 454,457, 458, 459, 460, 463, 466, 468, 471, 473, 474, 476, 478, 479, 480,482, 485, 486, 492, 493, 494, 495, 497, 498, 499, 500, 501, 503, 509,511, 512, 514, 515, 519, 522, 523, 527, 530, 532, 536, 537, 538, 539,541, 542, 545, 548, 549, 551, 552, 554, 555, 560, 562, 564, 565, 568,569, 574, 575, 577, 580, 583, 584, 587, 588, 589, 593, 594, 595, 597,598, 601, 603, 605, 609, 610, 612, 613, 614, 619, 621, 622, 623, 626,627, 628, 629, 630, 633, 635, 637, 639, 640, 641, 642, 643, 646, 647,648, 649, 650, 651, 652, 653, 656, 663, 664, 669, 674, 675, 677, 679,685, 690, 692, 693, 696, 697, 699, 700, 702, 704, 707, 709, 710, 711,714, 717, 718, 719, 720, 724, 726, 727, 729, 732, 743, 744, 747, 748,749, 751, 752, 753, 754, 756, 758, 759, 760, 762, 763, 764, 765, 766,767, 768, 769, 771, 775, 776, 777, 781, 782, 784, 785, 786, 787, 788,792, 794, 796, 797, 799, 801, 803, 804, 805, 806, 808, 810, 814, 818,822, 823, 824, 826, 829, 830, 831, 832, 835, 838, 840, 843, 845, 846,848, 850, 851, 852, 854, 857, 858, 864, 865, 866, 867, 869, 870, 871,872, 873, 875, 881, 883, 884, 886, 887, 891, 894, 895, 899, 902, 904,908, 909, 910, 911, 913, 914, 917, 920, 921, 923, 924, 926, 927, 932,934, 936, 937, 940, 941, 946, 947, 949, 952, 955, 956, 959, 960, 961,965, 966, 967, 969, 970, 973, 975, 977, 981, 982, 984, 985, 986, 991,993, 994, 995, 998, 999, 1000, 2, 6, 11, 13, 17, 26, 30, 36, 39, 47, 49,51, 54, 56, 58, 63, 65, 69, 73, 77, 81, 84, 90, 93, 95, 98, 100, 103,105, 109, 112, 119, 124, 130, 136, 138, 141, 146, 149, 154, 157, 159,163, 168, 172, 175, 178, 181, 187, 189, 191, 195, 201, 204, 207, 210,214, 220, 224, 228, 230, 232, 236, 239, 246, 248, 253, 260, 262, 264,266, 273, 283, 290, 296, 301, 304, 306, 312, 317, 319, 323, 326, 329,331, 334, 336, 341, 344, 351, 353, 356, 359, 370, 374, 378, 383, 385,389, 398, 402, 408, 411, 419, 421, 423, 426, 428, 430, 435, 437, 441,445, 449, 453, 456, 462, 465, 467, 470, 472, 475, 477, 481, 484, 491,496, 502, 508, 510, 513, 518, 521, 526, 529, 531, 535, 540, 544, 547,550, 553, 559, 561, 563, 567, 573, 576, 579, 582, 586, 592, 596, 600,602, 604, 608, 611, 618, 620, 625, 632, 634, 636, 638, 645, 655, 662,668, 673, 676, 678, 684, 689, 691, 695, 698, 701, 703, 706, 708, 713,716, 723, 725, 728, 731, 742, 746, 750, 755, 757, 761, 770, 774, 780,783, 791, 793, 795, 798, 800, 802, 807, 809, 813, 817, 821, 825, 828,834, 837, 839, 842, 844, 847, 849, 853, 856, 863, 868, 874, 880, 882,885, 890, 893, 898, 901, 903, 907, 912, 916, 919, 922, 925, 931, 933,935, 939, 945, 948, 951, 954, 958, 964, 968, 972, 974, 976, 980, 983,990, 992, 997, 1001, 1, 29, 35, 46, 68, 72, 76, 83, 89, 92, 97, 111,118, 135, 145, 148, 153, 156, 162, 171, 174, 186, 194, 200, 206, 209,213, 219, 227, 235, 245, 252, 259, 272, 282, 289, 295, 300, 311, 316,322, 333, 340, 343, 350, 358, 369, 373, 401, 407, 418, 440, 444, 448,455, 461, 464, 469, 483, 490, 507, 517, 520, 525, 528, 534, 543, 546,558, 566, 572, 578, 581, 585, 591, 599, 607, 617, 624, 631, 644, 654,661, 667, 672, 683, 688, 694, 705, 712, 715, 722, 730, 741, 745, 773,779, 790, 812, 816, 820, 827, 833, 836, 841, 855, 862, 879, 889, 892,897, 900, 906, 915, 918, 930, 938, 944, 950, 953, 957, 963, 971, 979,989, 996, 1002, 28, 34, 45, 67, 71, 75, 117, 134, 144, 152, 161, 185,199, 218, 234, 244, 288, 294, 299, 310, 315, 349, 368, 400, 406, 417,439, 443, 447, 489, 506, 516, 524, 533, 557, 571, 590, 606, 616, 660,666, 671, 682, 687, 721, 740, 772, 778, 789, 811, 815, 819, 861, 878,888, 896, 905, 929, 943, 962, 978, 988, 1003, 116, 133, 184, 198, 243,287, 293, 298, 309, 314, 367, 488, 505, 556, 570, 615, 659, 665, 670,681, 686, 739, 860, 877, 928, 942, 987, 1004, 115, 132, 286, 308, 366,487, 504, 658, 680, 738, 859, 876, 1005, 285, 365, 657, 737, 1006, 364,736, 1007, 363, 735, 1008, 362, 734, 1009, 361, 733, 1010 1000 11 0x94F999, 998, 995, 994, 993, 991, 986, 985, 984, 982, 981, 977, 975, 973,970, 969, 967, 966, 965, 961, 960, 959, 956, 955, 952, 949, 947, 946,941, 940, 937, 936, 934, 932, 927, 926, 924, 923, 921, 920, 917, 914,913, 911, 910, 909, 908, 904, 902, 899, 895, 894, 891, 887, 886, 884,883, 881, 875, 873, 872, 871, 870, 869, 867, 866, 865, 864, 858, 857,854, 852, 851, 850, 848, 846, 845, 843, 840, 838, 835, 832, 831, 830,829, 826, 824, 823, 822, 818, 814, 810, 808, 806, 805, 804, 803, 801,799, 797, 796, 794, 792, 788, 787, 786, 785, 784, 782, 781, 777, 776,775, 771, 769, 768, 767, 766, 765, 764, 763, 762, 760, 759, 758, 756,754, 753, 752, 751, 749, 748, 747, 744, 743, 732, 729, 727, 726, 724,720, 719, 718, 717, 714, 711, 710, 709, 707, 704, 702, 700, 699, 697,696, 693, 692, 690, 685, 679, 677, 675, 674, 669, 664, 663, 656, 653,652, 651, 650, 649, 648, 647, 646, 643, 642, 641, 640, 639, 637, 635,633, 630, 629, 628, 627, 626, 623, 622, 621, 619, 614, 613, 612, 610,609, 605, 603, 601, 598, 597, 595, 594, 593, 589, 588, 587, 584, 583,580, 577, 575, 574, 569, 568, 565, 564, 562, 560, 555, 554, 552, 551,549, 548, 545, 542, 541, 539, 538, 537, 536, 532, 530, 527, 523, 522,519, 515, 514, 512, 511, 509, 503, 501, 500, 499, 498, 497, 495, 494,493, 492, 486, 485, 482, 480, 479, 478, 476, 474, 473, 471, 468, 466,463, 460, 459, 458, 457, 454, 452, 451, 450, 446, 442, 438, 436, 434,433, 432, 431, 429, 427, 425, 424, 422, 420, 416, 415, 414, 413, 412,410, 409, 405, 404, 403, 399, 397, 396, 395, 394, 393, 392, 391, 390,388, 387, 386, 384, 382, 381, 380, 379, 377, 376, 375, 372, 371, 360,357, 355, 354, 352, 348, 347, 346, 345, 342, 339, 338, 337, 335, 332,330, 328, 327, 325, 324, 321, 320, 318, 313, 307, 305, 303, 302, 297,292, 291, 284, 281, 280, 279, 278, 277, 276, 275, 274, 271, 270, 269,268, 267, 265, 263, 261, 258, 257, 256, 255, 254, 251, 250, 249, 247,242, 241, 240, 238, 237, 233, 231, 229, 226, 225, 223, 222, 221, 217,216, 215, 212, 211, 208, 205, 203, 202, 197, 196, 193, 192, 190, 188,183, 182, 180, 179, 177, 176, 173, 170, 169, 167, 166, 165, 164, 160,158, 155, 151, 150, 147, 143, 142, 140, 139, 137, 131, 129, 128, 127,126, 125, 123, 122, 121, 120, 114, 113, 110, 108, 107, 106, 104, 102,101, 99, 96, 94, 91, 88, 87, 86, 85, 82, 80, 79, 78, 74, 70, 66, 64, 62,61, 60, 59, 57, 55, 53, 52, 50, 48, 44, 43, 42, 41, 40, 38, 37, 33, 32,31, 27, 25, 24, 23, 22, 21, 20, 19, 18, 16, 15, 14, 12, 10, 9, 8, 7, 5,4, 3, 0, 1000, 997, 992, 990, 983, 980, 976, 974, 972, 968, 964, 958,954, 951, 948, 945, 939, 935, 933, 931, 925, 922, 919, 916, 912, 907,903, 901, 898, 893, 890, 885, 882, 880, 874, 868, 863, 856, 853, 849,847, 844, 842, 839, 837, 834, 828, 825, 821, 817, 813, 809, 807, 802,800, 798, 795, 793, 791, 783, 780, 774, 770, 761, 757, 755, 750, 746,742, 731, 728, 725, 723, 716, 713, 708, 706, 703, 701, 698, 695, 691,689, 684, 678, 676, 673, 668, 662, 655, 645, 638, 636, 634, 632, 625,620, 618, 611, 608, 604, 602, 600, 596, 592, 586, 582, 579, 576, 573,567, 563, 561, 559, 553, 550, 547, 544, 540, 535, 531, 529, 526, 521,518, 513, 510, 508, 502, 496, 491, 484, 481, 477, 475, 472, 470, 467,465, 462, 456, 453, 449, 445, 441, 437, 435, 430, 428, 426, 423, 421,419, 411, 408, 402, 398, 389, 385, 383, 378, 374, 370, 359, 356, 353,351, 344, 341, 336, 334, 331, 329, 326, 323, 319, 317, 312, 306, 304,301, 296, 290, 283, 273, 266, 264, 262, 260, 253, 248, 246, 239, 236,232, 230, 228, 224, 220, 214, 210, 207, 204, 201, 195, 191, 189, 187,181, 178, 175, 172, 168, 163, 159, 157, 154, 149, 146, 141, 138, 136,130, 124, 119, 112, 109, 105, 103, 100, 98, 95, 93, 90, 84, 81, 77, 73,69, 65, 63, 58, 56, 54, 51, 49, 47, 39, 36, 30, 26, 17, 13, 11, 6, 2,1001, 996, 989, 979, 971, 963, 957, 953, 950, 944, 938, 930, 918, 915,906, 900, 897, 892, 889, 879, 862, 855, 841, 836, 833, 827, 820, 816,812, 790, 779, 773, 745, 741, 730, 722, 715, 712, 705, 694, 688, 683,672, 667, 661, 654, 644, 631, 624, 617, 607, 599, 591, 585, 581, 578,572, 566, 558, 546, 543, 534, 528, 525, 520, 517, 507, 490, 483, 469,464, 461, 455, 448, 444, 440, 418, 407, 401, 373, 369, 358, 350, 343,340, 333, 322, 316, 311, 300, 295, 289, 282, 272, 259, 252, 245, 235,227, 219, 213, 209, 206, 200, 194, 186, 174, 171, 162, 156, 153, 148,145, 135, 118, 111, 97, 92, 89, 83, 76, 72, 68, 46, 35, 29, 1, 1002,988, 978, 962, 943, 929, 905, 896, 888, 878, 861, 819, 815, 811, 789,778, 772, 740, 721, 687, 682, 671, 666, 660, 616, 606, 590, 571, 557,533, 524, 516, 506, 489, 447, 443, 439, 417, 406, 400, 368, 349, 315,310, 299, 294, 288, 244, 234, 218, 199, 185, 161, 152, 144, 134, 117,75, 71, 67, 45, 34, 28, 1003, 987, 942, 928, 877, 860, 739, 686, 681,670, 665, 659, 615, 570, 556, 505, 488, 367, 314, 309, 298, 293, 287,243, 198, 184, 133, 116, 1004, 876, 859, 738, 680, 658, 504, 487, 366,308, 286, 132, 115, 1005, 737, 657, 365, 285, 1006, 736, 364, 1007, 735,363, 1008, 734, 362, 1009, 733, 361, 1010 22 3 0xD 20, 17, 16, 15, 13,10, 9, 8, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24 223 0xD 17, 16, 15, 13, 20, 9, 10, 8, 19, 2, 21, 18, 6, 3, 1, 14, 12, 22,11, 0, 5, 7, 23, 4, 24 22 3 0xD 20, 17, 16, 15, 13, 9, 10, 8, 21, 2, 19,18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24 22 3 0xD 20, 17, 16, 15,9, 10, 8, 13, 21, 2, 19, 18, 6, 3, 1, 14, 12, 22, 11, 0, 5, 7, 23, 4, 24


13. A computer system, comprising a readable storage medium and acomputer program, wherein the encoding method according to claim 1 isimplemented when the computer program is executed by an encodingapparatus.
 14. A program product, wherein the program product comprisesa computer program, the computer program is stored in a readable storagemedium, and when at least one processor of an encoding apparatus readsthe computer program from the readable storage medium and executes thecomputer program, the encoding apparatus implements the encoding methodaccording to claim 1.